Comes from the phrase "To throw down the gauntlet", which means to issue a challenge. In medieval times a knight would throw his armored glove, or gauntlet, at the feet of another knight to challenge him to combat. If the knight took up the gauntlet he accepted the challenge.
1. You got a problem with me? Let's throwdown, right now!
2. He can really throwdown a beat.
3. "We're getting pizza. Are you in?" "Yea, I'll throwdown."