I just watched a trial at arms with a jousting match yesterday.

Yes, it can be dangerous. But far less than movies show. They wear specialized armor (wealthy knights owned parade armor, jousting armor, and battle armor). Weapons were not the same as they used in battle: not so sharp, lances of softer wood without metal tips, etc.

Another thing that is different from movies is that swords used by knights were not nearly as sharp as you think. If you and your opponent were wearing plate armor, the goal was to knock them over and then use the sharp tip to slide between plates (or use a dagger instead of the sword). That's why hammers, flails, maces, and axes were popular weapons. Not as aristocratic as a sword, but the blunt weapon with a larger contact area had a better chance of unbalancing an armored opponent and hurting them from impact damage.

Knights were at least in theory soldiers. Most of the activities in a tournament were part of their training routines. They participated because they gained status and were able to show off their prowess, and they were doing most of the same things as regular drills anyway.

eta: The typical format does not start with knights jousting at each other. In the skills course before the ORF jousts, for example, one challenge is to hit a shield on a stand with a sandbag as a counterweight. Miss the shield or ride too slow and get hit by the sandbag, and you get no points. The next challenge is to hit a small round target that is approximately the size of the tip of a lance hard enough to make it spin. If a rider misses these two challenges, they will not have enough points to advance to facing a live opponent. Warm-up games would weed out people unable to control their horse and hit a target, making sure those who did get to joust were prepared at least to a degree.