A charm is a magical spell or an object that brings luck: it's also a quality of being attractive and pleasing. To charm someone is to attract them.
There are several types of charms, but they mostly relate to attraction and good luck. A lucky coin is a charm. The spell of a witch that entrances you is a charm. People with magnetic personalities, who make you want to hang out with them, have charm and are therefore considered charming. Also, to charm someone is to attract them and win them over. Popular politicians charm the masses, and teachers' pets charm their teachers.