Kata were formulated in the most, part years in the past, and were the main method of karate teaching before, what became karate, left the Ryukyu islands to Japan.

Each style of Karate has there own Kata which may vary greatly in number. For example Goju Ryu schools for the most part study 12, Shotokan traditionally teaches 26, while a Shito Ryu system may teach over 40. Many of the Kata are related to each other and are merely derivatives of the same root, changing over time, some are unique to a system or school.

Purists argue that the study of too many Kata dilutes the art, while other say that every Kata can teach something different so a student should learn as many as possible. I guess it all depends on your point of view, but what can't be argued is that the performance of a kata takes practice, strength and stamina.

If you need to see the kata then follow the links below. These videos are of the official JKA kata (the so called "blue videos")so may differ from what you are taught if you are not in a close relative of what was once the JKA, but they are better than nothing. Also beware that they are being performed to illustrate the movements, therefore are not being performed with strictly the right timing.
Official JKA Kata videos