Islam has two major holidays, Eid Ul-Fitr (Post-Fasting Festival) and Eid Ul-Adha.
The word Eid itself is an Arabic word, whose root connotation is 'that which comes back, time after time, and rejoicing.' Its particular usage in Islam, for the two major holidays, is because these two days are meant to be days of rejoicing.
The Prophet Muhammad (Allah bless him and give him peace) said, "They are days of eating, drinking, and remembrance of God." [Reported by Bukhari in his Sahih, an authoritative collection of the sayings of the Prophet.]
In this same spirit, the Qur'an mentions: