Someone wayward is a little stubborn and independent — they're determined to find their own way and are not easily controlled.
Being wayward can mean a few things, but they all have something to do with doing your own thing — often, going against what others want you to do. A rebellious student is wayward. A son who ignores his parent's advice is wayward. A politician who goes against everyone else in his political party is wayward. Wayward folks like to go their own way — and they often take the unexpected path.