This shows a pretty good pic of a box squat. The key is to sit back and really recruit the hamstrings. I suggest the article by Dave Tate on this site entitled "Squatting from Head to Toe." It will really explain the box squat in great detail to you.
A dynamic box squat is simply a regular box squat performed with a submaximal load (usually around 50-60% of your max) in a very explosive manner. That is, you sit back, pause on the box and then explode upward as fast as possible.