Here is a complete explanation which is copied from Wikipedia.
("Eid al-Fitr is the Muslim holiday marking the breaking of fasting in the month of Ramadan. It is celebrated on the first day of the month of shawwal. It is also sometimes called 'the little festival', as opposed to, 'the great feast' aka feast of sacrifice; These two festivals being the main festive manifestations among Muslims. Eid is a gift from Allah (God) for the Muslims who sacrifice their every right in the month of Ramadan for the sake of Allah (God). After the first little Eid the Second Eid aka Great Feast comes after 2 months and 10 days, In Which Muslims sacrifice a Halal animal like Goat, Buffalo or Camel.")