The stator is the "stationary" part, with windings, that lies under the rotor, or the "rotational" part that revolves as the flywheel spins. The rotor/flywheel has the magnets around its inside diameter perimeter and the result of the magnets spinning around the windings produces AC current.
Your rectifier converts the AC current into useable DC voltage that is controlled or "regulated" by the OB's voltage regulator. Stators are specific to outboard motors (and other small engines).
In plain english, a stator is an important part in a system that acts as an alternator would on an inboard motor. Your outboard stator is the "powerhouse" of your outboards ignition system.