Driving by the superpowers he has, Finn, an old wise dog, who befriends Jake, a 12 year old boy, and wander around the world, fighting the evil and helping the innocence and the poor. Although they always face many terrible, they manage to overcome all the obstacles they face and do their work well.
It's one of those programs in which the littlest members of your brood won't get half the jokes. But that's what makes the show so beloved - it plays differently to different demos. Your kid will love the adventure, you'll get more of the dialogue.
There is a mad morality to many of the stories; some are downright warmhearted. Say what you will about Adventure Time, but its characters have more depth than many found in prime time.