A cyclocross course is usually set up in a relatively flat, muddy field with long straightaways and hairpin turns. There also may be paved roads or dirt roads involved. The course is short and the race is short - one hour plus one lap. Part of the course is usually singletrack in the woods, and there are obsticles that you can not ride over, such as barriers and staircases and steep hills and sand pits.

Skinny tires and a lightweight bike you can shoulder are faster than mountain bikes on this type of course, especially when it's dry and the speeds are high. Often there is a sprint finish, too, and you'll want drop bars and thin tires for that.

Some cross courses are more like mountain bike races, though, with mostly singletrack. Lots of people ride hardtail mtn bikes on such courses. Also, lots of beginner cross racers ride mtn bikes because they don't have cross bikes.