Comparison of static and dynamic lighting
Static lighting is best for objects that never move, especially with respect to their shadows.
Dynamic lights allow a shadow which is very crisp to update with changes in the model animation (both changes in deformation and changes in world position).
Static shadows are baked in place, and are only built once. Dynamic shadows are rendered on the fly, constantly updating as scene elements change.
In the real world, of course, all shadows would therefore come under the dynamic category, but that is quite expensive in a computed world, so static lighting's mission is to give us a fast render which, while looking nice comes with the limitation that it will only hold up if nothing is moving. The problem is that, in a game, lots of things move.
If you have ever placed a UTTeleporter in your level and wondered why it renders black, or not at all, you will have confronted the need for dynamic lighting. Some objects require a dynamic light to perform properly...