There are three main types of BMXing, Vert (Vertical), Street, and Dirt.
Vert is when you keep going up and down on a big U-shaped object made out of wood, it looks like this:
Just a lot bigger.
Street is when you do tricks on normal everyday things. (ex. Doing a grind on a handrail.) It could also be in a skatepark or doing tricks on nothing (ex. Bunnyhops).
Dirt is very simple to understand. It's just going off 10 foot dirt ramps, sometimes in a race, or sometimes to just do tricks.