Roleplaying is, at its heart, a form of improv. Of course there are many differences between improv and roleplaying, but when you look at the actual practice of each, you can see that they both live and breathe by the same basic principles, and they both crash and die when these principles are ignored.
"Improv" is an interactive performance art that requires a certain level of training and rigor. The audience pays the actors to appear on stage, and the actors shape their performance around cues from the audience. It's entirely spontaneous, and as you can imagine, it can be quite crazy for an actor, not knowing what's going to happen next.
To help with this, they use a special technique they call "Yes, and...?" which lets them handle whatever sorts of situations that might come up without getting thrown off-guard. Basically it means that each actor always accepts what the others say is true, and modifies the performance to go with whatever comes up. For example, if one actor says "hello mother" to another actor, now the one he spoke to is his mother for the duration of this scene. The "mother" accepts this new reality and offers something of her own in response, such as "Where have you been all night? Your father and I have been worried sick!" Alternatively if any actor denies what another actor just said or did, that's called "blocking," (as in, "No, I'm not your mother!") and it tends to stop the scene right there unless the initial actor can roll with it and accept it in his turn (as in, "Oh. I'm sorry... My mother was standing there a moment ago... I'm blind, you see...").