The old style of instructing martial arts is by teaching Kung Fu forms. This applies to Karate, Kung Fu, Taekwondo, Kenpo, and those kinds of arts. Even if you're not in a kata oriented school, however, there is a focus on the study of form.
The unfortunate fact is that most people don't know why they are studying in this manner. They don't see the connection between repetition of dance-like moves and real combat. The moves often even seem removed from any real function.
The first thing to understand is that the body is a form, and the dance is a form. Thus, when you move one, you move the other. The point here is that you are learning what you live in.
Most people are under the impression that they actually are a body, but the cold, hard fact is...they ain't. But they won't realize that unless they take control of that muscle and bone thing and start to move it. The best way to move that body is by doing taekwondo kata.
The second thing to understand is that forms are actually advanced movements. Advanced movements require either massive amounts of time invested, or they require a firm grasp of the basics. It is on this matter of perfecting basics that most people fall down on.
The third thing to realize is that you are stumbling through a murky realm, defining something that seems to have no shape. You continue studying these karate kata or taekwondo forms, and one day they will make total sense. This comes not because you have understood the dance-like steps, but because you have looked at your own body long enough to understand what it really is.
It is awareness that you are growing through this martial farce, the body and the mind are second to that. Awareness through the body, and extended to the universe. If you really want to understand what the martial arts are, and the real meanings of the forms, then you need ask yourself only one question: where does awareness come from.
The above having been noted, even after awareness is defined, one needs to discipline oneself to do the forms sufficient times to plumb the depths of oneself. You do the forms, day after day, year after year, and there will come a time you will wake to a new reality: a new you. Do Kung Fu forms enough, and one day you won't be doing the forms, you will be doing the art: you will be doing you.