Street is a style in which the biker is either riding in a place man made such as a course you may see on the X-games or in a area in a city that has rails, ledges, or ramps to do tricks on.

Dirt is the first form of B.M.X.  It is the original way of extreme biking.  This is usually done at track s or someone's personal trails. 

Vert is the newest form of B.M.X.  It evolved from the ramps used in street.  It is done on a half pipe.  Bikers originally used old sewer pipes to do vert jumping.