You can find links to some basic info on favorites here, specifically this post is rather detailed: How do favorite questions work?
This feature request has been posted on main meta a few year ago: Add a page explaining the favorites feature to the Help Center. Existence of this feature request suggests that you are probably not the only person who searched for information on favorites unsuccessfully in the help center.
Very briefly: If you favorite a question (click on the star next to it), then it is added to your favorite tab. The number near this star shows how many users favorited the particular question.
So basically all it does is that it helps you to create list of question which you want to have accessible somewhere and where you are able to follow relatively easily whether there have been any new activity (edits, new answers, new comments). So perhaps reasonable names for this feature could also be follow or bookmark, rather than favorite.
More often than not the users favorite question which are interesting to them. It seems that you are asking mainly why some users favorite low quality questions. There might be many reasons for this. Some examples I can think of:
- I voted to close this question, since it was unclear/low quality. If the user edits the question, I want to see that there were changes, so that I can vote to reopen if it was sufficiently improved.
- I downvoted the question - if the OP edits the question, I might remove my downvote. I favorited it so that I notice any changes.
- The question is poor, but one the answers contains information which is interesting to me. I want to keep the link somewhere, so I add it to my favorites.
- The question is likely to be deleted, which makes finding it again difficult. Since I want to keep the link because of rather interesting exchange in comments, I favorite the question.1
- This question is rather easy, but it suggest a generalization which seems rather intriguing about this. At the moment I do not have too much time to think about this - I will favorite this, so that when I check my favorites, I am reminded about this.
- This question is so poor that it definitely should be downvoted. I have already used all my 40 votes today, so I'll mark it and get back to it tomorrow.
1Deleted questions are still shown on favorite tab - but if I remember correctly only users who can see deleted question actually see the title of the question and the link. I have just favorited a few questions which seem likely to be deleted just to test this.
So that it is easier to examine low quality questions which are favorited (if somebody wants to), I have created these SEDE queries: Questions which are closed and favorited, Closed question with negative score which are favorited
In the cases where the question is favorited by single user, it might be the OP. Here is a SEDE query: Closed questions with negative score favorited only by the OP. If it is a relatively new and inexperienced user, it is quite plausible that sometimes they favorite their own question without really knowing what they are doing and how the favorites work.