You do not get reputation for closing questions.
You do not get badges for closing questions. (I think. If there is one that doesn't come to mind, then it's not the primary motivator for most people closing posts.)
For most people, they're voting to close to make the site, and thus indirectly the whole internet, a better place.
Closing questions really does help a lot in order to ensure quality content. A lot of time/effort has gone into working to determine what types of questions result in quality content and what does not, and to close questions that have a high probability of generating very low quality answers and a low probability of generating high quality answers.
It doesn't always seem obvious to new users (and even some old ones) just how profound of an improvement this can make, but as you spend more and more time on the site you really begin to notice questions that don't get closed that meet the close criteria and what actually happens to most of them. It's not pretty. It often takes a lot more time and effort to deal with the problems that arise from leaving these questions around than to just nip them in the bud right when they pop up. It's not only better for people curating the site or answering questions, but it's usually better for the person asking a question; having an opportunity to fix a problematic question without it being cluttered with very low quality answers makes it more likely to get good answers when it's finally improved.