Eid means recurring happiness or festivity. There are two such Eid in Islam. The first is called Eid al-Fitr (the Festival of Fast Breaking). It falls on the first day of Shawwaal, the tenth month of the Muslim year, following the month of Ramadhaan in which the Holy Qur’an was revealed and which is the month of fasting.
The second is called Eid al-Adhaa (the Festival of sacrifice). It falls on the tenth day of Zulhijjah, the final month of the Muslim year. The Islamic Eid are unique in every way. To them there can be nothing similar in any other religion or any other sociopolitical system. Besides their highly spiritual and moral characteristics, they have matchless qualities.
Each Eid is a wholesome celebration of a remarkable achievement of the individual Muslim in the service of Allah SWT. The first Eid comes after an entire month of 'absolute' fasting during the days of the month. The second Eid marks the completion of Hajj to Mecca, a course in which the Muslim handsomely demonstrates his renouncement of the mundane concerns and hearkens only to the eternal voice of Allah SWT.
Each Eid is a thanksgiving day where Muslims assemble in a brotherly and joyful atmosphere to offer their gratitude to Allah SWT for helping them to fulfill their spiritual obligations prior to the Eid. This form of thanksgiving is not confined to spiritual devotion and verbal expressions. It goes far beyond that to manifest itself in a handsome shape of social and humanitarian spirit. The Muslims who have completed the fasting of Ramadhaan express their thanks to Allah SWT by means of distributing alms among the poor and needy on the first Eid before the prayer.
From: www.islaam.org