In improv (the acting kind) there is something called "pimping". This is when you put your fellow comedian on the spot, either by giving them some unusual attribute (endowing) or calling for some difficult action ("Show us that dance routine you've been working on!") For beginners it's considered bad form, but experienced improvers will do this all the time. You may have seen the TV show Whose Line Is It, Anyway? where one by one the actors come to a party and are given some unusual trait? It's like that, but unexpected.
So how does knowing this improve your performance as an improv musician? Say you hear this on stage:
"I'm so happy to be a Bloboslovian!"
"That's great. Hey, how does that national anthem go again?"
Player One is being pimped. The first rule of improv is, you never deny the situation. Player One needs to start singing. Of course he or she can do this a capella but even better is for you to start playing some stately chords of the Bloboslovian national anthem.
In a sense, you're being pimped too. Player Two is saying, We need to hear a song now! and it's up to you to provide it. Why?
There's a scene in the movie Who Framed Roger Rabbit? where Eddie (the detective) and Roger have been handcuffed together for a while. Eddie is awkwardly filing at the chain and Roger slips off his side of the cuffs to help. Eddie, incredulous, says, "You mean you could have taken those off at anytime?" "Not at anytime," says Roger, "only when it was funny."
This is one of your guiding precepts: play when it's funny. If someone on stage wants to hear Bloboslovian national anthem, you play Onward, Bloboslovia. If someone gets arrested, maybe you play the theme to Dragnet.
But only if it's funny.