The "pick up coil" is that part of the ignition system that picks up on, and communicates to the ignitor, how fast the engine is turning over. It mounts inside the clutch housing, where it reacts to the pick up coil timing rotor(I'm interpreting from clymers here
). It then sends a pulse to the ignitor, so the ignitor knows when to send the spark to the plugs.
Clymers has the specifics regarding the test procedure, and what to look for.
Its a white two wire connector, with a grey, and a black/blue wire inside the left side cover. With the positive probe from the ohmmeter in the grey side, and the negative probe in the black/blue side of the connector on the pick up coil side of the connector, you should get a reading of 248 to 372 ohms. If its outside of those parameters, it should be replaced.
If it goes bad, it'd be like an open switch or break in a circuit. The ignitor might be just fine, but it won't send a spark because it doesn't know when to do it.