Watson's Biblical & Theological Dictionary 
On this appellation, Dr. Jennings observes, There is a very remarkable appellation which the Apostle Paul, after glorying in his being "of the stock of Israel, and of the tribe of Benjamin," applies to himself, namely, that he was "a Hebrew of the Hebrews," Php_3:5 . By this expression Godwin understands a Hebrew both by father's and mother's side. But if this be all that the phrase imports, there seems to be very little occasion for the Apostle's using it immediately after having declared, that he was "of the stock of Israel, and the tribe of Benjamin;" which, on Godwin's supposition, is the same as a Hebrew of the Hebrews; for the Jews were not allowed to marry out of their own nation; or if they sometimes married proselytes, yet their number was comparatively so small among them, especially while they were under oppression, as they were at that time by the Romans, that methinks Paul would hardly have mentioned it as a distinguishing privilege and honour, that neither of his parents were proselytes. It is therefore a much more probable sense, that a Hebrew of the Hebrews signifies a Hebrew both by nation and language, which multitudes of Abraham's posterity, in those days, were not; or one of the Hebrew Jews, who performed their public worship in the Hebrew tongue; for such were reckoned more honourable than the Hellenistic Jews, who in their dispersion having, in a manner, lost the Hebrew, used the Greek language in sacris, and read the Scripture out of the Septuagint version. We meet with this distinction among the converted Jews, in the Acts of the Apostles: "In those days, when the number of the disciples was multiplied, there arose a murmuring of the Grecians or Hellenists against the Hebrews," Acts 6:1 . This is what St. Paul probably meant by his being a Hebrew, as distinguished from an Israelite: "Are they Hebrews? So am I. Are they Israelites? So am I," 2 Corinthians 11:22 . In one sense, these were convertible terms, both signifying Jews by nation and religion; but in the sense just mentioned, there were many, in those days, who were Israelites, but not Hebrews. St. Paul was both, not only an Israelite by birth, but a Hebrew, and not a Hellenistic Jew. Godwin expresses himself inaccurately, when he says that those who lived in Palestine, and who, as using the Hebrew text in their public worship, were opposed to the ‘Ελληνισται , are called Hebrews, or Jews. For, though Hebrew and Jew are convertible terms, when opposed to Gentiles, as denoting the seed of Abraham, and professors of the Mosaic religion, see Jeremiah 34:9; yet, as opposed to the ‘Ελληνισται , they are not convertible terms, there being Hebrew Jews and Hellenistic Jews; for it is said, that when "they, who were scattered by the persecution that arose about Stephen, travelled into several countries, preaching the word to none but Jews only," yet they spoke, προς τους ‘Ελληνιστας , to the Hellenists or Grecians, Acts 11:19-20 . In order to confirm the sense which is here given of the word ‘Ελληνισται , in opposition to the appellation Hebrews, it is proper we should take notice of the distinction between the "Ελληνες and ‘Ελληνισται . The former were Greeks by nation, and as such distinguished from Jews, Acts 16:1; Acts 19:10; and the Greek empire having been rendered by Alexander in a manner universal, and their language being then the most common and general, the appellation Greeks is sometimes given to the whole Heathen world, or to all who were not Jews, Romans 1:16; Romans 2:9 . These Greeks, called ‘Ελληνικοι by Josephus, are always styled ‘Ελληνες in the New Testament. On which account Grotius, understanding by the ‘Ελληνισται , or "Grecians, to whom some of those who were dispersed on the persecution which arose about Stephen: preached the Lord Jesus," Acts 11:19-20 , Greeks by nation, concludes there is a mistake in the text, and alters it according to the Syriac and Vulgate versions: "Certe legendum, [it ought certainly to be read,] saith he, " προς τους Ελληνας ." So indeed the Alexandrian manuscript reads, but it is supported by no other copy. And this is decisive against it—that from the words immediately preceding, it is evident that these Grecians were by nation Jews, and not Greeks; it being expressly said, that those who were scattered on the persecution "preached the Gospel to the Jews only." And for the "Ελληνες , or Greeks mentioned in St. John's Gospel, as being come to Jerusalem at the passover to worship in the temple, John 12:20 , and likewise those mentioned in the Acts, as worshipping along with the Jews in the synagogues, Acts 14:1; Acts 18:4; they were doubtless Greeks by birth and nation, yet proselytes to the Jewish religion. There is a distinction made between Jews and proselytes, Acts 2:10; but none between Hebrews and proselytes, because a proselyte might be either a Hebrew or a Hellenist, according to the language in which he performed public worship. That the Hellenists or Grecians were Jews, is farther argued from the account we have, that when at Jerusalem St. Paul "disputed against the Grecians, they went about to slay him," Acts 9:29 , as the Jews at Damascus had done before, Acts 9:23 . Now had these Grecians been strangers of a different nation, it cannot be imagined they durst have attempted to kill a Jew, among his own countrymen, in the capital, and without a formal accusation of him before any of their tribunals. Upon the whole, the ‘Ελληνισται , or Grecians being Jews, who used the Greek tongue in their sacred exercises, the Hebrew Jews and Grecian Jews were distinguished in those days, in like manner as the Portuguese and Dutch Jews are among us, not so much by the place of their birth, (many being born in England, others abroad,) as by the language they use in their public prayers and sermons.
Among the wonderful dealings of God, says Dr. Neander, by which the coming of Christianity was prepared, must be placed the spreading of the Jews among the Greeks and Romans. Those among them who belonged to the Pharisees gave themselves much trouble to obtain proselytes; and the loss of respect for the old popular religion, and the unsatisfied religious wants of multitudes, farthered their views. Reverence for the national God of the Jews, as a mighty Being, and reverence for the secret sanctuary of the splendid temple of Jerusalem, had long gained admittance among the Heathen. Jewish goetae (enchanters, jugglers, &c) permitted themselves to make use of a thousand acts of delusion, in which they were very skilful, to make an impression of astonishment on the minds of those around them. Confidence in Judaism had in consequence made such wide progress, especially in large capital towns, that the Roman writers in the time of the first emperors openly complain of it; and Seneca, in his book upon superstition, said of the Jews, "The conquered have given laws to the conquerors." The Jewish proselyte-makers, "blind leaders of the blind,"
who had themselves no conception of the real nature of religion, could give to others no insight into it. They often allowed their converts to take up a kind of dead monotheism, and merely exchange one kind of superstition for another; they taught them, that, by the mere outward worship of one God, and outward ceremonials, they were sure of the grace of God, without requiring any change of life; and they gave to them only new means of silencing their conscience, and new support in the sins which they were unwilling to renounce: and hence our Saviour reproached these proselyte- makers, that they made their converts ten times more the children of hell, than they themselves were. But we must here accurately distinguish between the two classes of proselytes. The proselytes in the strict sense of the word, the proselytes, of righteousness, who underwent circumcision and took upon themselves the whole of the ceremonial law, were very different from the proselytes of the gate, who only bound themselves to renounce idolatry, to the worship of the one God, and to abstinence from all Heathenish excess, as well as from every thing which appeared to have any connection with idolatry. The former often embraced all the fanaticism and superstition of the Jews, and allowed themselves to be blindly led by their Jewish teachers. The more difficult it had been to them to subject themselves to the observance of the Jewish ceremonial law, necessarily so irksome to a Greek or a Roman, the less could they find it in their hearts to believe, that all this had been in vain, that they had obtained no advantage by it, and that they must renounce their presumed holiness. What Justin Martyr says to the Jews, holds good of these proselytes: "The proselytes not only do not believe, but they calumniate the name of Christ twice as much as you, and they wish to murder and torture us who believe on him, because they are desirous to resemble you in every thing." The proselytes of the gate, on the contrary, had taken many of the most admirable truths out of Judaism. Without becoming entirely Jews, they had become acquainted with the Holy Scriptures of the Jews, they had heard of the promised messenger from God, of the King armed with power from God, of whom a report had been spread, as Suetonius says in the life of Vespasian, over the whole of the east. Much of that which they had heard from their Jewish teachers, whose writings they had read, had remained dark to them, and they were still to seek in them. By the notions which they had received from the Jews, of one God, of the divine government of the world, of God's judgment, and of the Messiah, they were more prepared for the Gospel than other Heathens; and because they still thought that they had too little, because they had no determined religious system, and were curious after more instruction in divine things, and because they had not received many of the prejudices which swayed the Jews, they were more fitted to receive the Gospel than many of the Jews. From the very beginning they must have been attentive to the preaching of the Gospel, which secured to them, without making them Jews, a full share in the fulfilment of those promises of which the Jews had spoken to them. To these proselytes of the gate, (the φοβουμενοι τον Θεον , the ευσεβεις of the New Testament,) passed therefore, according to the Acts, the preaching of the Gospel, when it had been rejected by the blinded Jews; and here the seed of the divine word found a fitting soil in hearts desirous of holiness. There were, however, doubtless, among the proselytes of the gate, some who, wanting in proper earnestness in their search after religious truth, only desired, in every case, an easy road to heaven, which did not require any self-denial; and who, in order to be sure of being on the safe side, whether power and truth lay with the Jews or the Heathens, sometimes worshipped in the synagogue of Jehovah, sometimes in the temples of the gods, and who, therefore, fluttered in suspense between Judaism and Heathenism.
Charles Buck Theological Dictionary 
A term occurring in the Greek text of the New Testament, and which in the English version is rendered Grecians, Acts 6:1 . The critics are divided as to the signification of the word. Some observe, that it is not to be understood as signifying those of the religion of the Greeks, but those who spoke Greek. The authors of the Vulgate version render it like our Graeci; but Messieurs Du Port Royal, more accurately, Juifs Greca, Greek or Grecian Jews; it being the Jews who spoke Greek that are here treated of, and who are hereby distinguished from the Jews called Hebrews, that is, who spoke the Hebrew tongue of that time. The Hellenists, or Grecian Jews, were those who lived in Egypt, and other parts where the Greek tongue prevailed: it is to them we owe the Greek version of the Old Testament, commonly called the Septuagint, or that of the Seventy. Salmasius and Vossius are of a different sentiment with respect to the Hellenists: the latter will only have them to be those who adhered to the Grecian interests. Scaliger is represented in the Scaligerana as asserting the Hellenists to be the Jews who lived in Greece and other places, and who read the Greek Bible in their synagogues, and used the Greek language in sacris; and thus they were opposed to the Hebrew Jews, who performed their public worship in the Hebrew tongue; and in this sense St. Paul speaks of himself as a Hebrew of the Hebrews, Philippians 3:5-6 .i.e. a Hebrew both by nation and language. The Hellenists are thus properly distinguished from the Hellines, or Greeks, mentioned John 12:20 . who were Greeks by birth and nation, and yet proselytes to the Jewish religion.
Holman Bible Dictionary 
Hastings' Dictionary of the New Testament 
HELLENISTS. —See Grecians.
Morrish Bible Dictionary 
The Nuttall Encyclopedia 
Originally Jews who would fain have seen Jewish thought and life more or less transformed in spirit as well as fashion after a Greek pattern; eventually those who by contact with Greek civilisation became Grecianised, and were open to learn as much from the civilisation of the Greeks as was consistent with the maintenance in their integrity of the principles of their own religion.