Kata is the fundamental expression of complete mental, physical, and spiritual unity. The word kata means form, or shape. Basically, kata is a series of prearranged defensive and offensive movements, including intricate body motions, each of which is an actual response to one or more attackers. At its highest value levels, the martial artist "fights" these imaginary opponents in deadly earnest. It is worth noting, though, that almost every kata begins with a defensive blocking technique and this reinforces the philosophy of karate ni senti nashi (no first attack in karate).
Apart from increasing co-ordination, kata practice develops strength, tone, speed, balance, flexibility, and depending on the rate and duration of the student's practice, it can become good aerobic exercise as well.
A simple and easy kata is very important for developing the basics, and simple, basic kata should be practised by advanced students as well as beginners. An advanced student is able to see deeper and more subtle meanings in the basic kata, and by virtue of sound basics, is able to make simple kata look good. In contrast, having a beginner attempt a more complicated kata does not make the beginner look like anything more than a beginner.
Grace should be manifested in kata as a result of the person's refinement of the meaning expressed in the physical movements of kata, and should not be something artificially added to it. Since the beauty of a kata as a whole is the combination of its total qualities, it is impossible for gracefulness to be manifested without a great deal of practice and training.
Strictly speaking, there is no such thing as perfect kata, since as you advance in your level, your "imaginary" opponents will also advance in theirs. It is a continuous process of polishing and re-polishing.
The important point that should be stressed with regard to the nature of kata is the fact that it can be performed at ones own pace.
The elderly, who do not possess such power and speed any longer, may modify kata and perform according to a reduced capability. We all grow old, or something becomes physically weak due to illness or injury, in which case we may not wish to spar with young and strong students in practice. Kata, however, can be practised beneficially regardless of age. In this sense, kata is very personal; each individual expresses themself according to capability.