I'm confused about Git. I get that it's distributed in the sense that each developer has their own repository.
But my confusion comes when the developers sync their repositories. There has to be a centralized repository, right?
No. You can very much have N developers in your team, and sync between each other, pushing and pulling code from their respective repositories.
The "central" repo has technically no more significance than any other repo in the system.
However, having a single canonical repo that's considered "the main" or "the central" makes organizing that much easier, you know where to pull builds from, and what to run your tests against. So nearly all of the projects I've seen using Git use that paradigm.