The two Eids
Islam has two festivals. Eid al-Fitr marks the end of Ramadan, on the first of Shawwal. Eid al-Adha, the greater Eid, falls on the tenth of Dhul-Hijjah during the days of Hajj. Both begin with a special Eid prayer and are days of gratitude, charity, and family. When the Prophet, peace be upon him, came to Madinah and found people celebrating two days, he said: 'Allah has given you two days better than them: the day of al-Fitr and the day of al-Adha' (Sunan Abi Dawud 1134).
Why the dates shift
Because the Islamic calendar is lunar, the Eids move about eleven days earlier each Gregorian year. The exact day depends on the sighting of the new moon, so the calculated dates shown here may differ by a day from your local announcement.
Greetings and sunnah
Common greetings are 'Eid Mubarak' (blessed Eid) and 'Taqabbal Allahu minna wa minkum' (may Allah accept from us and from you). It is sunnah to bathe, wear one's best clothes, eat an odd number of dates before the Eid al-Fitr prayer, and take different routes to and from the prayer ground.