The term Yes And is a short hand reference to the concepts of Acceptance and Addition. These are core concepts of improv; actually the core concepts of improv. In an improvised scene, the players are building everything from scratch: setting, plot, and characters. It is critical that when one player defines some component of a scene (mimes an object, performs an action, refers to an event, or endows another player with some attribute), all the other players immediately accept that component as a real part of the scene.
For example, if I mime placing a table on the stage, it's important that any other players walk around the table rather than right through it. If my partners walk through the mimed table, then the audience can see there is a problem, but what do they believe as the scene goes forward - is there a table, or not?
Accepting that the table is now part of the scene is the YES.
Beyond just accepting the table, if my partner mimes adding a vase of flowers to the table, then the audience senses a more interesting environment. And there is a subtle expectation that this is an important table and worthy of attention.
Adding an object to the table is the AND.
I use the physical, mimed example to simplify the concept, but Yes And is even more important to endowments between the characters. If I say the line "you don't pay enough attention to our kids" to my partner, and the response is "that's because we don't have kids!", well that's funny, but where do we go from there? Do we have kids? Do we not have kids? What does the audience understand?
Instead, the line "that's because I've never liked our kids" accepts my original premise, and adds more information about the kids and the player's feelings about them. Now we can keep building the scene together. A good example of Yes And.
There are a lot of "rules of thumb" for improv, and they cover a range of styles and methods for generating scenes. They're not necessarily hard and fast rules, and most can be creatively broken from time to time. But the concept of Yes And is a core concept to all of improv. Few things can shut down a scene quicker than not accepting, and a scene without additon will often seem lost or random. I'll talk about how Blocking and Denying - the opposite of Yes And - can drag down a scene in another post.