What is the difference between a 2 and a 4 stroke dirt bike?

Well with out boring you to death Ill give you the basic version.

A 2 stroke engines piston on the down stroke pulls in fuel and air mixture on the way up it compresses mixture. At the peak of the stroke it is combusted forcing piston down. On the pistons up stroke the exhaust port opens and pushes out exhaust out. If you count the cycles there are 2 hence 2 stroke. The piston makes 2 cycles for every power cycle. The 4 stroke makes 4 cycles for every power cycle.