Learn Hardcore Japanese: ame no hi ha tosyokan ga itumo yori aite imasu. - On rainy days, the library is less crowded than usual.

の links two nouns, so 雨の日 literally means a rain day or a day of rain. In natural English, that becomes a rainy day or on rainy days.

This noun + の + noun pattern is very common in Japanese:

日本の会社 = a Japanese company
夏の日 = a summer day
雨の日 = a rainy day

So here, 雨 modifies 日.

Why is there a は after 雨の日?

The は marks 雨の日 as the topic or setting of the sentence.

So 雨の日は gives the sense of:

as for rainy days...
on rainy days...

It sets the condition under which the rest of the sentence is true. This is very natural in Japanese when talking about time, situations, or categories.

Why is 図書館 marked with が instead of は?