“Many a” is often used as an adjective to describe an indefinite large number.
A few more examples:
I've told you many a time not to ride your bike on the pavement. (many a time=many times)
Many a true word is spoken in jest. (Saying; many good things)
There's many a slip twixt(between) cup and lip. (Saying; to emphasize that many bad things might happen before something is completed)