This word denotes the special privileges and advantages belonging to the first-born son among the Jews. He became the priest of the family. Thus Reuben was the first-born of the patriarchs, and so the priesthood of the tribes belonged to him. That honour was, however, transferred by God from Reuben to Levi (Numbers 3:12,13; 8:18).
The first-born son had allotted to him also a double portion of the paternal inheritance (Deuteronomy 21:15-17). Reuben was, because of his undutiful conduct, deprived of his birth-right (Genesis 49:4; 1 Chronicles 5:1). Esau transferred his birth-right to Jacob (Genesis 25:33).
The first-born inherited the judicial authority of his father, whatever it might be (2 Chronicles 21:3). By divine appointment, however, David excluded Adonijah in favour of Solomon.
The Jews attached a sacred importance to the rank of "first-born" and "first-begotten" as applied to the Messiah (Romans 8:29; Colossians 1:18; Hebrews 1:4-6). As first-born he has an inheritance superior to his brethren, and is the alone true priest.
These dictionary topics are from M.G. Easton M.A., D.D., Illustrated Bible Dictionary, Third Edition, published by Thomas Nelson, 1897. Public Domain, copy freely.
Easton, Matthew George. "Entry for 'Birthright'". "Easton's Bible Dictionary".