Learn French: Avril et mai sont des mois de fêtes. - April and May are months of celebrations.

In French, the names of months and days of the week are not capitalized. Avril only has a capital letter here because it is the very first word of the sentence.

The English translation just says 'are months', so why is there a des before mois?

In French, nouns almost always need an article in front of them to show gender and number. Des is the plural of un and une. While we usually skip this word in English, French requires des to show that you are talking about an unspecified plural amount (similar to saying 'some months').

Is mois spelled the same way in the singular?

Yes! Because the singular word mois already ends in an -s, its spelling does not change in the plural. You can tell it is plural in this sentence because of the plural article des and the plural verb sont.

Why is it de fêtes and not des fêtes if the word for celebrations is plural?

When you connect two nouns and the second one simply describes the type or category of the first, you just use the short connecting word de. You do not use des because you are not talking about specific celebrations, you are just describing what kind of months they are.