There are many different types of biking events. Below are some details on a few:
Freeride trails:
Freeride trails often make use of natural terrain in order to fabricate stunts, examples being dropoffs and narrow ladder bridges ("skinnies"). Riders also build large ramps to throw the cyclist into the air. As freeride bikes are so durable they are often overly hefty and have far too much suspension to be effectively ridden uphill, so it is quite common to use a lift to take you to the top of the hill, or to push your bike uphill. Similarly, Downhill Mountain Biking often requires riders pushing their specially designed bikes up hill or using a lift to get to the starting line.
4X / Mountain Cross / 4-cross racing:
This is quite a new way to ride. 4 riders race downhill on a track - simply a race to see who gets there first.
North Shore mountain biking:
This type of mountain biking originated in the steep and wet terrain of rocky Vancouver, on the North Shore of Canada. Due to the difficult, if not totally impossible terrain, riders had to build bridges over inpassable areas, like rocks, roots and stumps etc. This practive then evolved into making man-made complex stunts, which can often be extremely challenging to manoeuvre a bike over.