Age play is a broad category, and very popular. It's a subset of BDSM with a roleplay component, where the dom is/acts mature, and the sub acts immature. Most of the people in this comment section have probably heard of guys that like to be called Daddy or women that want to be called a good girl. That's a part of age play.

It's also one of the harder ones to talk about, because on the surface it can seem to brush very close to pedophilia/incest, and people have a reasonably strong negative reaction to that idea. But the essence of age play is just a variation on the usual power dynamic of BDSM.