The festivals which are prescribed in Islam are Eid al-Fitr and Eid al-Adha, and the weekly Eid of Jumuah. There is no other festival in Islam apart from these three.
Eid al-Fitr takes place after the end of the Month of Ramadan (i.e on the 1st of shawwal which is the 10th month of the Islamic calendar)
Eid al-Adhaa is the tenth day of Dhool-Hijjah, the last (twelfth) month of the Hijri or Islamic calendar. It is, as the Prophet (peace be upon him) said: The greatest day in the sight of Allaah, may He be blessed and exalted, the Day of Sacrifice . . . (Reported by Abu Dawud; see also Saheeh al-Jaami, 1064).
It is also the greatest day of Hajj, as the Prophet (peace be upon him) told us. (Reported by al-Tirmidhi, see Saheeh al-Jaami, 8191).
The reason why it is described as the greatest day of the year is that it combines so many acts of worship which are not combined on any other day, such as the Eid prayer, offering the sacrifice, reciting Takbeer (glorifying Allaah), and widespread remembrance of Allaah. For the pilgrims in Makkah, it also includes offering a sacrifice, stoning the pillars representing Shaytaan (the devil), shaving the head (for men only; women merely cut a little off their hair), and performing Tawaaf (circumambulation of the Kabah) and Saee (running between the two hills of Safaa and Marwa).