1. The best evolution of the cycling form. Unlike just riding to get from point A to point B, BMX involves whatever you feel like adding. See a good driveway curb and bust out some air with style off of it.
2. A sport (bicycle motocross) which evolved from motocross racing (aka: dirt biking) which involves racing on a dirt track with berms and jumps on a bicycle. Two major sacntioning bodies exist today. The ABA (American Bicycle Association) and the NBL (National Bicycle League).
3. Usually a 20" (can be 24") wheeled bicycle designed to ride on dirt trails, jumps, street obstacles, or skateparks. Not a kids bike or dirt bike.
I went to the skatepark on my BMX bike to ride and the lame skaters who run the place said they don't allow BMX at their park