Dynamic equilibrium usually refers to chemical equations, in which both the forward and reverse directions are possible. When the system is in equilibrium, it isn't that the products in the forward direction are no longer being produced, or that the backward reaction is no longer occurring either. When it is in dynamic equilibrium, both the forward and reverse reactions are both still going on, but at equal rates, so you see no net change.
Static equilibrium can be used for several things, but physics comes to mind. I'll keep using chemistry though to explain. If you have a reaction that can only occur in one direction, you can reach equilibrium when you have used up the limiting reagent (whatever you have in lowest quantity). Since the reactions stop occuring, you are in Static equilibrium.
I hope that helped. If you need further explanation, please let me know.