Puberty is more than the development of sex organs, or the buildup of hormones. It is the first real defining time of a human's existence. During puberty, a teenager will often choose their vocation. They will, in most cases, know what they like, for puberty is a time of discovery.
While in puberty, the mind changes, as well. All through junior high and high school, teenagers are very picky - they'll go through liking five different kinds of music, hanging out with three different crowds, and god only knows how many girlfriends or boyfriends they'll have!
And then, after puberty ends, around the end of high school, the teenagers' friends all change. They lose interest in their best friends. They change their minds about who is "cool" and who isn't. They become "adult", in a way, and everything changes. They go off to college, and hang out with their new crowd. Puberty is clearly more than just a sexual change - it's a mental one, and a philosophical one as well.