Ali was the son of Abu Talib, a prominent Quraish chief and custodian of the Holy Kaaba. Abu Talib was so called because he was the father of "Talib", the eldest brother of Ali. The real name of Abu Talib was Abd Manaf. He was however more popularly known by his surname than by his real name. Abu Talib was the son of Abdul Muttalib. Abdul Muttalib was also a surname, his real name being Shaybah. Abdul Muttalib was the son of Hashim. Hashim was a great man of the line, and his descendants came to be known as Hashimites.
The mother of Ali was Fatima. She was the daughter of Asad who was a son of Hashim. Fatima was a cousin of Abu Talib. Thus both the father and mother of Ali were Hashimites, and that was a great honor.