If your distributor is mounted on the engine, then the oil pump is most likely driven by the crankshaft. The oil pump provides pressurized oil to the bearings and other moving parts in the engine.
The distributor may have a drive gear that meshes with a gear on the end of the camshaft, or it may be directly driven by an eccentric on the camshaft. In either case, as long as the distributor is turning, it will turn the oil pump.