A certain incident occurred during the life of Prophet Muhammed (PBUH&HP) about 3 years after first receiving revelations from the Angel Gabriel (AS). Muhammed was commanded by God to proclaim the message of Islam publicly, so he walked up a nearby hill near the houses of the Quraish tribe in Mecca and called out to all the people to come.
This raised area was used to warn the towns' people if they were under attack from a nearby tribe or if some other harm was coming their way, so when Muhammed called out to the people he knew they would all be shocked and come running to him to see what was behind the hill.
So they came in a rush and asked him why he had called them. Muhammed asked them 'If I said a large army is about to attack us, then would you believe me?', the people said yes, indeed you are most truthful - we know that you are one of the truthful ones.
Muhammed then explained that there was no such army but he had something important to say, something much more important than an attacking army. Then he began to tell them about the principle beliefs of Islam, of his Prophethood and that he was a Messenger of God sent to stop the people from polytheism and to guide them to the path of the one and only God. The people listened attentively, but not all people took it lightly.
Among the crowd was his uncle Abu Lahab (Father of fire), so called because of his fiery anger and his reddish complexion, and he was very annoyed with what Muhammed had done. He said to Muhammed after listening to the initial few words the Prophet said, 'Is this what you called us out here for?!! May you perish/be destroyed (Tabban laka)'.
Muhammed was surprised by this response and remained silent. God was very angered by the insult and he sent these verses to Muhammed -
Surat Al Masad || The Flame In the Name of Allah Most Gracious Most Merciful [111.1] Perdition (Tabbat) overtake both hands of Abu Lahab, and he will perish. [111.2] His wealth and what he earns will not avail him. [111.3] He shall soon burn in fire that flames, [111.4] And his wife, the bearer of fuel, [111.5] Upon her neck a halter of strongly twisted rope.
Abu Lahab was an avowed enemy to Muhammed from the very beginning and so was his wife, hence the curse upon her too.