The story behind Eid ul-Adha
Muslims believe that God revealed in a dream to Ibrahim (Prophet Abraham) to sacrifice his son Isma’il. Ibrahim and Isma’il set off to Mina for the sacrifice. As they went, the devil attempted to persuade Ibrahim to disobey God and not to sacrifice his beloved son. But Ibrahim stayed true to God, and drove the devil away. As Ibrahim prepared to sacrifice his son, God stopped him and gave him a sheep to sacrifice instead. The story is also a part of the other Abrahamic religions (see the Binding of Isaac).
Observing Eid ul-Adha
It is celebrated on the 10th day of the month of Dhul Hijja (ذو الحجة) of the lunar Islamic calendar, after Hajj, the annual pilgrimage to Mecca in Saudi Arabia. This happens to be approximately 70 days after the end of the month of Ramadan.
While Eid ul-Fitr is considered to be three days, Eid ul-Adha is supposed to be four days. The first day is the primary holiday, on which men, women, and children are expected to dress in their finest clothing and perform prayer (Salah) in a large congregation. Muslims who can afford to do so sacrifice domestic animals, usually sheep, as a symbol of Ibrahim's sacrifice; this sacrifice is called "Qurbani." The meat is distributed amongst their neighbors, relatives, and the poor and hungry. The charitable instincts of the Muslim community are demonstrated during Eid ul-Adha by the concerted effort to see that no impoverished Muslim is left without sacrificial food during this day. Coming immediately after the Day of Arafat (when Muhammad pronounced the final seal on the religion of Islam), Eid ul-Adha gives concrete realization to what the Muslim community ethic means in practice.
Update - 1/13/2005: Please read malik's comment on this post and visit his site, Eid Mubarak. Thank you, malik!