Look at these examples:
Note that when talking about doing something on a celebration day, you can use either:
à + [celebration]
or
le jour de + [celebration].
or
le jour de + [celebration].
While à is more general (i.e. at Christmas), le jour de insists a bit more on the very day (i.e. on Christmas Day).
Case of Eid = l'Aïd
As Aïd starts with a vowel, we use à l' or le jour de l', in order to ease the pronunciation.
Also see Using prepositions with name days, like Saint Valentine's Day
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