From the Eid al-Fitr Wikipedia page:
Eid al-Fitr (the "festival of breaking of the fast") is an important religious holiday celebrated by Muslims worldwide that marks the end of Ramadan, the Islamic holy month of fasting (sawm). The religious Eid is a single day during which Muslims are not permitted to fast. The holiday celebrates the conclusion of the 29 or 30 days of dawn-to-sunset fasting during the entire month of Ramadan. The day of Eid, therefore, falls on the first day of the month of Shawwal. The date for the start of any lunar Hijri month varies based on the observation of new moon by local religious authorities, so the exact day of celebration varies by locality.
Eid al-Fitr has a particular Salat (Islamic prayer) consisting of two Rakats (units) and generally offered in an open field or large hall. It may be performed only in congregation (Jama’at) and has an additional extra six Takbirs (raising of the hands to the ears while saying "Allāhu Akbar", literally "God is great"), three of them in the beginning of the first raka'ah and three of them just before Ruku' in the second raka'ah in the Hanafi school of Sunni Islam. Other Sunni schools usually have twelve Takbirs, seven in the first, and five at the beginning of the second raka'ah. This Eid al-Fitr salat is, depending on which juristic opinion is followed, Fard فرض (obligatory), Mustahabb مستحب (strongly recommended, just short of obligatory) or mandoob مندوب (preferable).
Muslims believe that they are commanded by Allah, as mentioned in the Quran, to continue their fast until the last day of Ramadan and pay the Zakat and fitra before offering the Eid prayers.