Abu Lahab, meaning "Father of Flames", was the nickname of Abdul-Uzza, the son of Abdul Muttalib, one of the brothers of Muhammad's father Abdullah. Abu Lahab succeeded Muhammad's uncle, Abu Talib, as the head of Hashim tribe. Abu Talib protected Muhammad while he was alive, and Abu Lahab revoked that protection. al-Lahab 111:1-3, see Sahih Bukhari 2.477
The curse against Abu Lahab in Sura 111 has been turned into a Muslim argument for the divine origin of the Qur'an by viewing it as a prophecy, see the discussion in the section Are there Prophecies in the Qur'an?
The origin of the nickname "Abu Lahab" seems to be a matter of speculation.
... he was called Abu Lahab because his cheeks were always red or inflamed. (Wikipedia, Abu Lahab, 29 March 2011)
Thus Abu Lahab (father of flames) means the possessor of flames or a man of fiery temperament, that is, one in whom the flames of anger and envy rage furiously. So, by extension, anyone who entertains enmity and hostility to the truth in his heart and who consequently burns with the flames of anger and rage can be called Abu Lahab. (Source, 29 March 2011)
Note, however, that neither of these claims is supported with references to original sources.