The word 'Eid is an Arabic name to mean a festivity, a celebration, a recurring happiness, and a feast. In Islam, there are two major 'Eids namely the feast of Ramadhan ('EId Al-Fitr) and the Feast of Sacrifice ('Eid Al-Adhha). The first 'Eid is celebrated by Muslims after fasting the month of Ramadhan as a matter of thanks and gratitude to Almighty Allah. It takes place on the first day of Shawwal, the tenth month of the lunar calendar. The second 'Eid is the Feast of Sacrifice and it is to be celebrated for the memory of prophet Ibrahim trying to sacrifice his son Isma'il(Ishmael). This 'Eid lasts four days between the tenth and the thirteenth day of Zul-Hijjah, the twelfth month of the lunar calendar.
It was narrated that Jubayr ibn Nufayr said: When the companions of the Messenger of Allaah (peace and blessings of Allaah be upon him) met one another on the day of Eid, they would say to one another: “Taqabbal Allaahu minna wa mink (May Allaah accept (this worship) from us and from you).” Al-Haafiz said: Its isnaad is hasan.
For more details, see Islam Awareness Homepage: https://www.islamawareness.net/Eid/