Improvisational comedy is comedy created in the now. There is no time to think of what to do, one must just do it. Generally there are 3 "rules" in improvisational comedy.
1. Yes, and
Referring to the spirit in which the scenes take place. You ideally agree with what you partner says and then add something to it. (Note: Try yes, and'ing your friends and family you'll be surprised how good it feels..)
2. Don't ask questions
This is a general rule of thumb. Experienced improvisers can ask questions and still build a scene together. Inexperienced improvisers will find themselves caught in circles that don't forward the scene.
3. Never Deny
You may never deny the reality which is established by you or your partner. If someone says "Hey Doc, your wife died by the river a few minutes ago" The other performer should not say "I don't have a wife" or "She's not dead"
There are two styles of improvisational comedy, Short Form Improv and Long Form Improv.
Some excellent books to read on the subject are The Compass, Something Wonderful Right Away, Truth in Comedy, Improvisation for the Theater, Impro and Impro for Storytellers.