To do it well.
To expand the boundaries of the form. To excel. To create something wonderful, surprising, unique, solid and fun. To solve a different tantalizing puzzle each time.
To connect on a deep level with your teammates. To do a thing that you and they can be proud of.
To imagine the best improvisers on the planet, to imagine that they are watching your every performance, and to imagine that they are proud of you, as well.
For me, that's about it.
"But, what about just having a good old time and not caring about how well you do it? What about not taking it seriously? What about just plain horsing around for the fun of it and nothing else?"
Maybe, but not for me. I can mess around and have mindless fun by playing beer pong, riding a thrill ride, liking memes or engaging in a mashed potato fight. I don't buy a piano to bang on it with my fists or push it off the top of a building. Kind of a waste of a perfectly good piano.
I don't believe that something needs to be mindless to be fun. In fact, since fun is all in the mind, I think the mind ought to be involved in the process. So, I tend to take performance improv (as opposed to therapeutic improv or casual improv jams which are not strictly about performance) seriously. People spend much cash and time on improv lessons, workshops, seminars and books. If you've done that, then you know what I mean.
Embrace the discipline that is improv. Try to do it well. "Fine" is an insult, not a compliment. "Good enough"...never really is. Kicking down sand castles is a type of fun. But building them is where it's at. If your team isn't serious about improv but you are, find or create a new team asap.
Mark Twain once wrote: "The secret source of humor is not joy but sorrow; there is no humor in Heaven."
If you're here, you take improv seriously. Don't stop! Enjoy your efforts. And delight in your accomplishments.