It's something that was only put on American-Market Peugeot mopeds. DOT required it.
Have you ever been listening to the radio while your friend is revving a moped? Points ignitions can cause huge radio-wave disturbance. That coil is meant to "react" with the points ignition to cancel out disturbance.
If you've been having ignition troubles, there is a lot of documentation on here about the peugeot ignition problem. That reactance coil is not your problem, but you can disconnect the white wire to bypass it if it bothers you.
Basically, replace the coil on your stator with a puch (or any bosch) ignition coil. Then have fun trying to time the bike without a woodruff key.