Boyd’s Bible Dictionary:

( father of abundance). Son of Ahimelech, and fourth high priest in descent from Eli, of the line of Ithamar, younger son of Aaron (1 Sam. 23:99And David knew that Saul secretly practised mischief against him; and he said to Abiathar the priest, Bring hither the ephod. (1 Samuel 23:9)), only one of Ahimelech’s sons who escaped the vengeance of Saul in the slaughter at Nob (1 Sam. 22:19-20). Fled to David at Keilah, and became a high priest. Deprived of the high priesthood by Solomon. For fuller history read 1 Sam. 22 to 1 Kings 3.

Concise Bible Dictionary:

Son of Ahimelech the high priest. He escaped from the slaughter of the priests executed by Doeg at the command of Saul (1 Sam. 22:18,2018And the king said to Doeg, Turn thou, and fall upon the priests. And Doeg the Edomite turned, and he fell upon the priests, and slew on that day fourscore and five persons that did wear a linen ephod. (1 Samuel 22:18)
20And one of the sons of Ahimelech the son of Ahitub, named Abiathar, escaped, and fled after David. (1 Samuel 22:20)
). He became an adherent of David, and was acknowledged as high priest; but becoming involved in Adonijah’s rebellion he was deprived of the priesthood by Solomon and sent to dwell in the city of Anathoth which belonged to the sons of Aaron (1 Kings 2:2626And unto Abiathar the priest said the king, Get thee to Anathoth, unto thine own fields; for thou art worthy of death: but I will not at this time put thee to death, because thou barest the ark of the Lord God before David my father, and because thou hast been afflicted in all wherein my father was afflicted. (1 Kings 2:26); 1 Chron. 6:6060And out of the tribe of Benjamin; Geba with her suburbs, and Alemeth with her suburbs, and Anathoth with her suburbs. All their cities throughout their families were thirteen cities. (1 Chronicles 6:60)). In 1 Kings 4:4,4And Benaiah the son of Jehoiada was over the host: and Zadok and Abiathar were the priests: (1 Kings 4:4) Abiathar is named with Zadok as priests (not the priests); though deposed, Abiathar was still a priest. There is a difficulty in 2 Samuel 8:1717And Zadok the son of Ahitub, and Ahimelech the son of Abiathar, were the priests; and Seraiah was the scribe; (2 Samuel 8:17) and 1 Chronicles 18:1616And Zadok the son of Ahitub, and Abimelech the son of Abiathar, were the priests; and Shavsha was scribe; (1 Chronicles 18:16) where Ahimelech (or Abimelech) the son of Abiathar is named as priest with Zadok in the time of David. Some suppose that the names should be transposed, and that Abiathar is meant; but this Ahimelech may have been a son of the above — named Abiathar (it not being at all unusual to name a son after his grandfather) and for some reason he is mentioned in these passages as priest instead of his father. He may have been a more worthy man than his father, who was thrust out of the priesthood for his own sin, though it fulfilled the prophecy concerning the house of Eli in Shiloh (1 Sam. 2:31-3631Behold, the days come, that I will cut off thine arm, and the arm of thy father's house, that there shall not be an old man in thine house. 32And thou shalt see an enemy in my habitation, in all the wealth which God shall give Israel: and there shall not be an old man in thine house for ever. 33And the man of thine, whom I shall not cut off from mine altar, shall be to consume thine eyes, and to grieve thine heart: and all the increase of thine house shall die in the flower of their age. 34And this shall be a sign unto thee, that shall come upon thy two sons, on Hophni and Phinehas; in one day they shall die both of them. 35And I will raise me up a faithful priest, that shall do according to that which is in mine heart and in my mind: and I will build him a sure house; and he shall walk before mine anointed for ever. 36And it shall come to pass, that every one that is left in thine house shall come and crouch to him for a piece of silver and a morsel of bread, and shall say, Put me, I pray thee, into one of the priests' offices, that I may eat a piece of bread. (1 Samuel 2:31‑36); 1 Kings 2:2727So Solomon thrust out Abiathar from being priest unto the Lord; that he might fulfil the word of the Lord, which he spake concerning the house of Eli in Shiloh. (1 Kings 2:27)). Our Lord in Mark 2:2626How he went into the house of God in the days of Abiathar the high priest, and did eat the showbread, which is not lawful to eat but for the priests, and gave also to them which were with him? (Mark 2:26) speaks of Abiathar as high priest, in connection with David eating the showbread, doubtless because he afterward attained to that office.

Strong’s Dictionary of Hebrew Words:

contracted from 1 and 3498; father of abundance (i.e. liberal); Ebjathar, an Israelite
KJV Usage:

Jackson’s Dictionary of Scripture Proper Names:

father of abundance or "father of a remnant"

Potts’ Bible Proper Names:

Excellent, or surviving father; father of abundance:―son of Ahimelech, 1 Sam. 22:20. {Pater superstes mansit}