A "deadpan" style of humor is a way of telling jokes where you don't change your expression. You just make the joke with a straight (serious) face.

"Deadpan" and "dry" are very similar ways to describe humor. English speakers more often use "dry" to describe the sense of humor of someone that they know, while "deadpan" is specifically for talking about the technique of telling a joke, and use more often to talk about a professional comedian or actor.