The flywheel is a large metal drum with magnets attached along the inside rim. The flywheel is usually connected to the crank, and rotates when the crank is turned (the crank is turned when you start a moped, as well as while the moped is running). The flywheel rotates around the stator plate, also sometimes called the magneto. Typically, ignition and lighting coils are located on the stator plate. These coils are literally coils of copper wire. The magnets rotating around these coils generates electricity due to electromagnetic induction. This electricity is what powers most electrical components on a moped, if there is not a battery present in the electrical system.
To hold the flywheel from turning (and thus often to prevent the crank from turning) buy a cheap chain wrench from Northern tool.
Here's a video on YouTube about how to remove a flywheel without the puller. For reviews of this method, please search the forums.