David Wells, from Netlify, and I take a crack at answering this question in an understandable way.
Are there still servers involved? Of course, but you don't manage them, scale them, or pay for them when you aren't using them. It really is a different model that deserves a new name.
Better yet, they enable front-end developers like us to do more than we ever thought we could. We'll cover a variety of use cases that might get you thinking.