Not a stupid question at all, and to be honest something I really struggle with. Stopwords are somewhat important because the results are different based on the search the user enters.
For example (real), I have a page and the title is "The Writer's Stop at Disney's Hollywood Studios". My site ranks differently based on the following permutations.
The Writer's Stop at Disney's Hollywood Studios = Position 10
Writer's Stop at Disney's Hollywood Studios = Position 12
Writer's Stop Disney's Hollywood Studios = Position 14
Interestingly removing the apostrophe's didn't appear to affect the search results. Only one test, so nothing conclusive I guess.
Ultimately my titles etc contain the proper phrase because from a user perspective it makes more sense.