It's easier to show than to explain, so I'm going to stick in a Youtube video here.
(Video from horsescanter's channel).
As you can see, the head goes down and the rear end comes up. Sometimes the horse will bounce off of all feet and spin in the air.
A horse bucks to get something off its back...which in domestic horses often means you. (Some horses may pop a little buck out of excitement...there used to be a top show jumper who would buck three times after every clear round he jumped!).
Most commonly, horses buck because they are in pain, badly spooked, or fed up with their rider for some reason. Bucking is most often caused by ill-fitting tack. It's also fairly common for a horse to buck the first time a saddle is put on its back (and sometimes the first time a rider gets on). But some horses will buck just because they're "mad" with their rider and want to get them off. Which has happened to me a few times. I also knew a pony who would try to buck people off into the manure heap or the nearest mud puddle. He definitely aimed and he was more likely to do it if you were wearing something light colored. Nasty sense of humor, perhaps?
Broncos are specifically bred and trained to be really good at bucking cowboys off. I'll talk about that at some point when I get into rodeos.