To enchant is to cast a spell over someone, like a witch might do. It also means to attract or catch someone's attention in a less mystical way.
Enchanting has a few meanings, but they all involve seduction. A witch or warlock enchants people they wish to influence through magic spells. A real person enchants in different ways: through jokes, good looks, and charisma. Not only people, but also engrossing songs or shows can be said "to enchant."