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.
static equilibrium is comparable to standing still on a tight rope and balancing yourself by sticking your hands out. Your static in the sense that you aren't moving and are in equilibrium: no net change in position.
dynamic equilibrium is comparable to a free fall. Eventually because of air resistance you will reach terminal velocity and will fall no faster. At this point you will be in dynamic equilibrium: no change in velocity, but dynamic in the sense that you are moving.
Yeah, essentially the state of equilibrium occurs when there is no net force acting on the object in question. This implies an acceleration of zero. Which in turn implies that either the velocity is zero, or is constant.
Another physics example of dynamic equilibrium is someone walking up an escalator the wrong way, at just the same rate as the escalator - so to an outside observer it appears that the person is stationary, while in reality he is in dynamic equib.