Answer by Allan Clews:
They Select Well
Stage hypnotists bring a whole group of people up to the stage and then send most of them back because they are looking for a few key things. Twenty-percent of the population are extremely hypnotizable (and it is a continuum so twenty-percent are not that hypnotizable and the rest fall somewhere in the middle). So the most important thing a stage hypnotist is looking for are people who can slip into a trance very easily. The most hypnotizable people can even often be identified by a certain glassy/watery look in their eyes.
They Test for Compliancy
The second thing they do is subject the group of volunteers to 'compliancy tests'. They may ask participants to stand this way or that way or put their hands up and do various things. They are looking for those who comply without hesitation and follow their orders.
They Find the Entertainers
The third thing they look for are people who are secretly or not-so-secretly exhibitionists and entertainers. I knew someone who was flabbergasted when his shy and inhibited friend stole a stage hypnotist's show. His friend couldn't talk to a group of women to save his life and there he was dancing around, doing a striptease and all sorts of other hilarious antics. I asked this person if his friend was a clown and an entertainer when they were alone together. The answer was, of course, yes. But then as a hypnotist I know that even the shyest person is never shy around their closest friends and family.
So this means that the stage hypnotists selects their participants very carefully. They also do it very quickly and turn it into part of the show with special jokes and other techniques.
They End by Giving Plausible Deniability
As to participants remembering what they did, let me say that it is possible to help someone develop a state of amnesia while in hypnosis. But this is not a simple procedure and requires certain suggestions and testing and retesting to make sure. This means it is extremely rare for someone to forget what they did on stage.
However, at the end of the show the hypnotist will give all the participants 'plausible deniability'. They will say to those who were on stage that they will not remember what they did and so when the participants return to their seats they can claim they didn't remember. The hypnotist said so and therefore their denial is plausible. And the more they deny this the more reinforcing it becomes.
However, researchers have taken these people aside and asked them privately and most admit they remember.
I should also add professional hypnotists love and hate stage hypnotists. We hate them because they are taking an profound tool and making a joke out of it. While we love them because our phones always ring and little more in the days after a stage hypnotist passes through town town.
And finally to answer your question: it feels fun and uninhibiting. You get to go up on stage and make people laugh and have a lot of fun doing so.