Hastings' Dictionary of the New Testament 
1 . The greatness of Christ .—Greatness is an attribute which more than once in the Scriptures is applied to Jesus Christ. It is used both relatively, in passages which suggest a comparison between His powers and those of such OT heroes as Jacob ( John 4:12), Jonah and Solomon ( Matthew 12:41-42), and Abraham or the prophets ( John 8:53); and in an absolute sense, with reference to the esteem in which He was to be held in the eyes of Jehovah ( Luke 1:32). In the teaching of Jesus Himself, however, greatness is less a status than a quality. In the few words in which He alludes to His own human greatness, He makes it to consist in capacity for service and for sacrifice ( Mark 10:45 ||), and it is significant that in the Epistles also the attribute is ascribed to Him only where the idea of service and sacrifice is prominent in the context ( Hebrews 4:14; Hebrews 10:21; Hebrews 13:20).
In one passage the greatness of the Son is compared with that of the Father ( John 14:28). This is admittedly a difficult saying. The important point to be borne in mind is that the statement must not be interpreted apart from the rest of Christ’s teaching concerning His relationship to the First Person in the Trinity. A careful study of His whole attitude seems to show that, whether He is here referring to such inferiority as is involved in His possessing the Divine essence by communication or to that which belonged to His subordination as being incarnate upon the earth, the words ‘are perfectly consistent with the belief in the unity of the Divine nature, and therefore with the belief in the equality of the Godhead of the Son with the Godhead of the Father’ (Westcott, ad loc. ; cf. Godet, ad loc. ).
2. The greatness of Christ’s followers .—Christ has less to say about His own greatness than about that of His followers. For there is a greatness that belongs to His Kingdom, and this He covets for each one of them. So exalted is it that it surpasses the highest conception of greatness hitherto received ( Matthew 11:11 = Luke 7:28). But this greatness of the Kingdom differs essentially from that in which the world delights. The world has confused greatness itself with certain caricatures of it known as ‘fame’ and ‘power.’ The teaching of Jesus draws clear lines of distinction.
( a ) Greatness is not fame . Men’s fame consists in what others say about them; Christians’ greatness consists in what they themselves are. Of the former consideration Christ bids His followers to be exultingly independent ( Matthew 5:11-12, note the strong word ἀγαλλιᾶσθε). Indeed, to share in their Lord’s greatness will involve not praise but persecution ( John 15:20). But upon the second consideration, that is to say, upon their character, their claim to greatness wholly depends. And the character demanded includes, not the assertive qualities of notoriety, but the milder attributes of childlike humility ( Mark 9:34, Matthew 18:1; Matthew 18:4, Luke 9:48), and obedience to the Divine law ( Matthew 5:19—a passage which has an important bearing on the relationship of the new dispensation to the old).
( b ) Greatness is not power . This, it is true, is the current conception of it. In the world’s view, to be great is to be able to exact from others as much as is possible of respect and service. The more servants a man has at his disposal, the wider the sphere in which he can command obedience, the greater he is held to be ( Mark 10:42 ||). Such was also the disciples’ conception. Two of them were ambitious of sitting the one on Christ’s right hand and the other on His left in His Kingdom; the others were jealous, because they coveted these seats of authority for themselves ( Mark 10:35 ff. = Matthew 20:20 ff.). In striking contrast with this view Jesus places His own pronouncement on greatness. According to His teaching as well as His example (see above), to be great is not to exact, but to give, as much service as possible. A man’s greatness is measured less by the service he commands than by the service he renders ( Mark 10:43-45 ||). In a glorious paradox the highest in the Kingdom is he who assumes the lowest place ( Matthew 23:11, John 13:14-16, and, for the supreme example, Philippians 2:5-11).
The practical importance of such teaching can scarcely be over-emphasized. Until the time of the Incarnation the position of a servant was the lowest of all; but when the Son of God appeared, He, in St. Paul’s words, ‘took the form of a servant’ (μορφὴν δούλου, Philippians 2:7), and from that day the whole status of honourable service, in whatever capacity, has been consecrated and raised. The position it occupies is no longer menial; it is the most exalted of all. The servant’s life, indeed, may be a life of greatness , inasmuch as Christ has placed the very essence of greatness no longer in power to command, but in willingness to minister. The very title which our Lord uses of Himself in appealing to His own example ( Mark 10:45 ||), suggests that the nearer a man’s life approaches to the ideal of humanity, the more completely will he realize his greatness in the service of others.
The exact significance of the title ‘Son of Man’ (wh. see) has been much discussed. To the present writer the truest explanation appears to be that which makes it point to Christ as the ideal of humanity. That is to say, He was not only a man, but also the perfect representation of mankind. There was nothing in Him that is foreign to ideal human nature, nor anything lacking that belongs to it. He was, if we may so express it, the perfect specimen of what man was intended to be. It will be seen that, if this view is correct, the application of the title made above is justifiable.
One more saying of Jesus must be included in our study. To His followers, as we have shown, greatness does not mean power in any earthly sense. And yet the very men who refuse to exert such power shall be possessed by a power superior to all earthly might—the power of the Father’s protection ( John 10:29—according to the probable reading).
Baker's Evangelical Dictionary of Biblical Theology 
Something or someone that is larger in size, quality, or quantity may be called "great." It is a term used for something beyond the ordinary. In the Bible, God, humans, and Christ receive this designation with theological significance.
God . The Bible describes God as the greatest of gods ( Deuteronomy 10:17 ); his greatness is unsearchable ( Psalm 145:3 ). In discussing this theological characteristic of God, how do we understand an attribute that is not understandable? Its very abundance makes our task difficult ( Psalm 150:2 ).
God by nature is great. The Bible affirms the greatness of his power ( Job 23:6; Psalm 66:3; Ephesians 1:19 ). Strength and might describe him ( Isaiah 40:26; 63:1 ). The "greatness of majesty" becomes the worshiper's cry for who God is ( Exodus 15:7; Deuteronomy 5:24 ).
Of course, the clearest view of God's greatness comes from his actions toward creation, especially toward his people. Creation records his greatness and leads to our praise ( Psalm 145:6 ). God's care of the children of Israel in the wilderness demonstrated his greatness ( Deuteronomy 3:24; 11:2 ). When Jesus healed a boy suffering from demon possession, the people affirmed the greatness of God in the act ( Luke 9:43 ).
God also exhibits greatness in love toward humanity by forgiving ( Numbers 14:19 ) and by redeeming ( Deuteronomy 9:26 ). Nehemiah asks God to remember him for his attempt to preserve the holiness of Israel. The basis for his request revolves around the greatness of God's lovingkindness ( Nehemiah 13:22 ).
As an attribute, the greatness of God describes the extent and magnitude of his qualities.
Humans . Humans also may be considered "great." After the plagues of Egypt, Moses was "great" in importance both in Egypt and among the people of Israel. The queen of Sheba attested to the great wisdom of Solomon ( 2 Chronicles 9:6 ). Nebuchadnezzar's greatness returned to him after he humbled himself before the Lord ( Daniel 4:36 ). Mordecai achieved greatness in his position in the Persian government ( Esther 10:2 ).
Human greatness depends on the quality of a person's life. It is something that may be taken away, as in the case of Nebuchadnezzar, or may be lost, as in the case of the greatness of the nation of Egypt ( Ezekiel 31 ). "Great folly" takes away any semblance of greatness ( Proverbs 5:23 ).
Psalm 71 explains that the actions of some enemies, perhaps due to old age, may lead to lost prestige. The psalmist's prayer attests to a trust in God to restore the former "greatness" (v. 21). Right standing in the community will be restored in the same way that God worked before the difficulties that took them away.
Christ . Christ turned the definition of human greatness in a profound direction. Jesus modeled greatness by humbling himself in coming to earth and dying on the cross ( Philippians 2:5-11 ). Jesus made this perspective clear in his teachings. When the disciples asked who is the greatest in the kingdom, Jesus answered by bringing a child into their midst and declaring that even admission into the kingdom depended on a similar attitude of humility ( Matthew 18:1-4 ).
The mother of James and John asked if her boys could sit on the right and left hands of Jesus in the kingdom. The other disciples became upset with the brothers. Jesus used the occasion to say that the one who wanted to be great among them had to be their servant ( Matthew 20:26; 23:11 ). Jesus noted that his life would exemplify this attitude by his service, including the gift of his life ( Matthew 20:28 ).
The greatness of a person is measured by service to others. Christ set the example.
G. Michael Hagan
See also God
Vine's Expository Dictionary of NT Words 
akin to megas (see Great , No. 1), is said of the power of God, in Ephesians 1:19 .
denotes "expressed greatness," 2—Corinthians 4:7; 12:7 . see Excel , B, No. 1.
King James Dictionary 
GREATNESS, n. Largeness of bulk, dimensions, number or quantity as the greatness of a mountain, of an edifice, of a multitude, or of a sum of money. With reference to solid bodies, however, we more generally use bulk, size, extent or magnitude than greatness as the bulk or size of the body the extent of the ocean the magnitude of the sun or of the earth.
1. Large amount extent as the greatness of a reward. 2. High degree as the greatness of virtue or vice. 3. High rank or place elevation dignity distinction eminence power command. 4. Swelling pride affected state.
It is not of pride or greatness that he cometh not aboard your ships.
5. Magnanimity elevation of sentiment nobleness as greatness of mind.
Virtue is the only solid basis of greatness.
6. Strength or extent of intellectual faculties as the greatness of genius. 7. Large extent or variety as the greatness of a man's acquisitions. 8. Grandeur pomp magnificence.
Greatness with Timon dwells in such a draught,
As brings all Brobdignag before your thought.
9. Force intensity as the greatness of sound, of passion, heat, &c.