Going to a comedy show is a bit like going to a fairground. You generally know what you're in for, you know that it is likely to be safe, you expect it to be amusing, and you expect there to be variety and surprise.
You may not like every ride. Some rides will be for you, some won't. Some rides might be more suitable for those with less of a nervous disposition, some family friendly, some horrifying. There may be some rides that you are familiar with and yet still enjoy, and others which you have not experienced before. You might like these unfamiliar rides, you might not.
The comedians are the tour guides, and the rides are the jokes. The comedian has to entice you onto the ride by making it look interesting and worth the time and bother. The ride then has to be enjoyable, and have a level of surprise. Some rides are like a long winding entertaining tale that ends in a sudden enthralling drop, so are enjoyable along the way and surprising at the end. Others are more short and abrupt, and just as you are getting used to the ride it goes off in multiple different directions with many surprises.
If the comedian gets it right by enticing you onto the best rides, keeping it interesting, and keeping it surprising, then you will know they're in a safe pair of hands and trust them enough to go on more of their rides. If the comedian misjudges and entices the you onto a ride that don't suit you, you might not want to go on another one. If the rides are too long without being interesting along the way, you may lost interest and want to get off before the surprise. If the rides don't have enough of a surprise element, you might not bother getting onboard another ride.
So to sum up my magical fairground theory of comedy, the comedian's job is to: