Shounen anime is a subset of the larger Japanese animation genre. It refers to anime genres which appeal primarily to pre-teens, or teenage boys. These are usually either action cartoons with dynamic plots and characters, or gameshows where the goal is for contestants to win prizes (such as toys) in order to win related contests.
Some examples of shounen anime could be Naruto, Bleach, One Piece, Dragon Ball Z, Detective Conan (Case Closed), Yu-Gi-Oh!, Pokemon and Hunter X Hunter. Most shounen anime have little nudity or romance tho there are some exceptions such as certain episodes in Fruits Basket (to get around censorship laws).