Every team needs a practical joker, and a party animal, but for the Teen Titans, they have a more literal one. Beast Boy was once a member of the Doom Patrol, an intergalactic peacekeeping team, but after an incident, he left the team to become more experience and become his own being. He met the Titans, and the rest is history.
Beast Boy is very lax, and likes to chill and have fun. But, when the time comes, he can be as serious as anyone. He's stopped numerous foes just by talking to them, and has even gotten so angry that he's scared the other Titans.
But the arc he's arguably most known for is the Terra arc, where he fell in love with a girl named Terra, who was actually a plant by Deathstroke, and their relationship took many turns over the course of that arc.
As an alien, Beast Boy can shapeshift into any animal, even alien ones. He can go big, go small, even go microscopic. He may not always be bright, but you could argue that Beast Boy has the biggest heart of the group.