From BiblePortal Wikipedia

Webster's Dictionary [1]

(1): ( a.) The exclusive right of inheritance which belongs to the eldest son. Thus in England the right of inheriting the estate of the father belongs to the eldest son, and in the royal family the eldest son of the sovereign is entitled to the throne by primogeniture. In exceptional cases, among the female children, the crown descends by right of primogeniture to the eldest daughter only and her issue.

(2): ( a.) The state of being the firstborn of the same parents; seniority by birth among children of the same family.

International Standard Bible Encyclopedia [2]

prı̄ - mṓ - jen´i - tū́r ( בּכורה , bekhōrāh , from bekhōr , "firstborn," from bākhar , "to act early"; πρωτοτόκια , prōtotókia ):

1. Recognition of Doctrine:

The right of the firstborn to inherit the headship of the family, carrying with it certain property rights and usually such titles as those of the high-priesthood or kingship. The writings of the Hebrews take for granted the recognition of a doctrine of primogeniture from the earliest times. In the most ancient genealogies a distinction is drawn between the firstborn and the other son ( Genesis 10:15;  Genesis 22:21;  Genesis 25:13;  Genesis 35:23;  Genesis 36:15 ). In the bestowal of parental blessings in patriarchal times great importance was attached to preferring the firstborn ( Genesis 25:31;  Genesis 27:29;  Genesis 48:13;  Genesis 49:3 ). The feud between Jacob and Esau (Gen 27:1 through 28:21) grew out of the stealing of the firstborn's blessing by the younger brother. Joseph was displeased when, in his blessing, Jacob seemed to prefer Ephraim to Manasseh, his firstborn ( Genesis 48:18 ). The father in such cases seems to have had the right to transfer the birthright from one son to another, from the days of Abraham in the case of Ishmael and Isaac, through those of Jacob in the matter of Reuben and Joseph and in the matter of Ephraim and Manasseh, down to the days of David in the selection of a successor to the kingship. Nevertheless, the Mosaic code, which declared (rather than enacted) the law of primogeniture, prohibited the abuse of this parental privilege in the case of a younger son by a favorite wife ( Deuteronomy 21:16 f).

2. The Double Portion:

The manner of acknowledging the firstborn incidentally referred to in Dt is "by giving him a double portion of all that he hath" ( Deuteronomy 21:17 ), that is to say, double the share of each of the other brothers. Jewish tradition ( Bekhō . 46a, 47b, 51a, 51b; Bābhā' Bathrā' 122a, 122b, 123a, 124a, 142b) accepts and elaborates on this right of the firstborn son. Thus, it applies only to the firstborn and not the eldest surviving son; it does not apply to daughters; it has reference only to the paternal estate, and not to the inheritance left by a mother or other relative, nor to improvements or accessions made to an estate after the death of the father.

3. Reasons for the Custom:

The object of the doctrine may be that the eldest son might be enabled to preside over the affairs of family with proper dignity, or that he might assume additional responsibilities, such as the support of unmarried sisters. Hence, one's birthright could be waived or sold ( Genesis 25:31 ,  Genesis 25:34 ). On the other hand it may be based in the ultimate analysis on the primitive feeling of favoritism for the firstborn reflected in the disappointment of Jacob, when he speaks of Reuben as his firstborn, his might, and the beginning of his strength ( rē'shı̄th 'ōn ,  Genesis 49:3; compare  Deuteronomy 21:17 ). This theory would be in accord with the right of the parent to transfer the right to a younger son. The suggestion of favoritism conveyed by the Hebrew bekhōr is manifested in its figurative use: of Israel ( Exodus 4:22 ), of Ephraim ( Jeremiah 31:9 ), of one dearly beloved ( Zechariah 12:10 ); (compare figurative usage in the New Testament:   Romans 8:29;  Hebrews 12:23;  Hebrews 1:6;  Revelation 1:5 ).

4. The Firstborn in Ancient Society; Sacrifice and Redemption:

Light is thrown on the attitude of the ancient world toward the firstborn, and hence, on the history of primogeniture, by the language used in connection with the plague of the firstborn: "from the first-born of Pharaoh that sitteth upon his throne, even unto the first-born of the maidservant that is behind the mill" or "the captive that was in the dungeon." Apparently no more dreadful catastrophe for all classes of society could be thought of than this slaying of the firstborn ( Exodus 11:5;  Exodus 12:29 ). The misguided fervor of the ancient Semites who offered their firstborn as the thing most dearly beloved as a sacrifice to their gods must be considered in this light, whether it appears among the Moabites, the Phoenicians or the Hebrews themselves ( Jeremiah 32:35;  Ezekiel 20:26 ,  Ezekiel 20:31;  2 Chronicles 28:3 ). It is difficult to predicate a connection between the basis of the doctrine of primogeniture and that of the Redemption of the First-born , other than that both are ultimately based on the importance of a firstborn son and the fondness of his parents for him. It is interesting to note, however, that the tradition of redemption and the law of primogeniture are kept so distinct that, while the latter has reference only to the firstborn of a father, the former has reference only to the firstborn of a mother ( Bekhō , viii. l, 46a; compare peṭer reḥem , "whatsoever openeth the womb,"  Exodus 13:2 ). In a polygamous society such as that presupposed in Dt 21 it is natural to suppose that the distinction between paternal and maternal primogeniture would be clearly before the minds of the people. See Birthright; Firstborn .

Cyclopedia of Biblical, Theological and Ecclesiastical Literature [3]

(denoted in Hebrews by בְּכיֹרָה : Sept. Πρωτοτόκια ,  Genesis 25:31;  Genesis 25:34;  Genesis 27:26;  Deuteronomy 21:17;  1 Chronicles 5:1; in the New Test. only in  Hebrews 12:16; A. V. "birthright"). Πρωτότοκος , always rendered "first-born" in the English version, is found in the Sept. in  Genesis 4:4;  Deuteronomy 21:17, and several other passages of the Old Test., as the representative of the Hebrew בְּכוֹר , signifying "one who openeth the womb," whether an only child, or whether other children follow. "Primogenitus est, non post quem alii, sedl ante quem nullus alius genitus" (Pareus). Πρωτότοκος is found nine times in the New Test. viz.  Matthew 1:25 (if the passage be genuine, and not introduced from the parallel passage in Luke);  Luke 2:7;  Romans 8:29;  Colossians 1:15;  Colossians 1:18;  Hebrews 1:6;  Hebrews 11:28;  Hebrews 12:23;  Revelation 1:5. Except in the Gospels, and  Hebrews 11:28, the word always bears a metaphorical sense in the New Test., being generally synonymous with heir or lord, and having, in  Hebrews 1:6, an especial reference to our Lord's Messianic dignity. In  Hebrews 12:23, "the assembly of the first-born," it seems to be synonymous with "elect," or "dearly beloved," in which sense it is also used on one occasion in the Old Test. ( Jeremiah 31:9).

In the 4th century, Helvidius among the Latins, an. Eunomius among the Greeks, wished to attach a signification to Πρωτότοκος , in Matthew 1 and Luke 2, different from the Old-Test. usage, maintaining, in order to support their hypothesis-viz. that Joseph and Mary had children after the birth of our Lord-that the word Πρωτότοκος , by reason of its etymology, could not be applied to an Only Child . Jerome replied to the former by appealing to the usage of the word in the Old Test. ( Adv. Helvid. In  Matthew 1:9). The assertion of Eunomius was equally refuted by the Greek fathers Basil (Hom. in Nat.), Theophylact (in Luke 2), and Damascenus (De Fid. Othod. 1. 4). In reference to this controversy, Drusius (Ad difficiliora loca Num c. 6) observes: "Sic sane Christus vocatur Πρωτότοκος , licet mater ejus nullos alios postea liberos habuerit. Notet hoc juventus propter Helvidium, qui ex ea voce inferebat Mariam ex Josepho post Christum natum plures filios suscepisse." "Those entitled to the prerogative" (viz. of birthright), observes Campbell ( On The Gospels ), "were invariably denominated the first-born, whether the parents had issue afterwards or not." Eunomius further maintains, from  Colossians 1:15, that our Lord was "a creature;" but his arguments were replied to by Basil and Theophylact. Some of the fathers referred this passage to Christ's pre-existence, others to his baptism. In  Isaiah 14:30, the "first-born of the poor" signifies the poorest of all; and in  Job 18:13. the "first-born of death" means the most terrible of deaths. It is noteworthy that in our Lord's genealogy the line is frequently- carried through a younger son (Seth, Shem, Abraham, Isaac, Jacob, Judah, David, Solomon, Nathan, etc.). (See First-Born).