First, let me break down the terminology.
- The word "Eid" in Arabic, just means "celebration" or "festival."
- "Fitr" means "breaking the fast" and "Adha" means "sacrifice."
Therefore, Eid ul-Fitr means the Festival of the Breaking of the Fast and Eid ul-Adha means the Festival of the Sacrifice. Eid ul-Fitr takes place after the month of Ramadan ends. Ramadan is the month of fasting for Muslims. During the month of Ramadan, Muslims must fast every day from dawn till dusk. This obligation is one of the Five Pillars of Islam.
Muslims celebrate the end of the month of Ramadan with Eid ul-Fitr, hence the name. Eid ul-Adha takes place during the Hajj season. The Hajj is a pilgrimage Muslims must make to the Kaaba in the city of Mecca in modern day Saudi Arabia. All Muslims are required to complete this journey at least once in their lifetime if they are able to. The Hajj is also one of the Five Pillars of Islam.
During the Hajj, the pilgrims sacrifice a sheep. Both the Old Testament and the Quran mention a story where Abraham was ordered to sacrifice his son by God. Jews and Christians believe this son was Isaac, but most Muslims believe this son was Ishmael. When Abraham showed he loved God enough to sacrifice his son on command, God ordered a sheep be sacrificed instead and spared Ishmael. The sacrifice in Hajj is to commemorate this event. And Eid ul-Adha, the Festival of the Sacrifice, also celebrates this event.
Both Eid ul-Fitr and Eid ul-Adha are celebrated in similar fashion.
Muslims start the day early and go to a common meeting place, usually a mosque or open field. There they make a special prayer followed by a short sermon from the Imam (leader). They then gather for special meals, meeting with family and friends, and giving charity and gifts. The only difference is that during Eid ul-Adha, the Festival of the Sacrifice, it is common for a sheep, goat, cow, or camel to be slaughtered as well. While there are other holidays celebrated by Muslims, none of them are as universally accepted as Eid ul-Adha and Eid ul-Fitr.