Body skill

I have previously written about how I think of martial arts training as having two poles

1. Kata: Pre-arranged, cooperative practice (includes: sets, forms, drills)
2. Randori: Competitive, sportive, game-like, chaotic practice (includes: sparring, games) 

Taking the metaphor further, and visualizing these poles as the north and south poles of the world of martial arts training, one can explore the rest of the surface, with extreme structure and extreme chaos as the poles, and all other training methods in-between.  This article talks a bit about one way to move from cooperative combinations towards randori, step-by-step.  There are many, many such approaches to practice.

Regardless of the method or methods of practice, the aim is to train the mind and body to internalize martial arts skill and ability.  The japanese term tai-jitsu (body art) captures some of the flavor of this; in chinese gong fu or kung fu (mastery from long practice) is arguably a closer match.

Physical attributes must be trained (broadly: conditioning) -- body; and coordination refined and knowledge acquired -- mind.  The mix, order and priority varies between martial arts, styles and schools.  For example: high kicks will demand considerable leg flexibility, strength, and balance; skill in joint-locks require anatomical knowledge, fluid movement, and sensitivity.

In terms of training methods, there are different schools of thought about training holistically or component-wise, directly and indirectly, incrementally or by successive refinement.