The inyo is presently used as the symbol of the Japan Karate Association, although other corporations have used this symbol as well.
The inyo is the Japanese equivalent to the Chinese yin yang symbol. Both of these symbols represent the universe as a circle. Inside the circle, the two colors co-exist, together yet separate. The colors represent the two types of energies, positive and negative. In (yin in Chinese) represents the negative element. It is passive, weak, empty, dark, feminine, cold, etc. Yo (yang in Chinese) signifies the positive element. It is active, strong, full, light, masculine, hot, etc. Although these forces are opposites, each one cannot exist without its counterpart.
When viewing the yin yang symbol, the S-shaped curve in the center should give the feeling of movement or blending. When viewing the inyo, one should have the feeling of the red circle actually rising, again giving the feeling that all is not static.
Sometimes, the inyo is referred to as "the symbol of the rising sun." If you look at the Japanese flag, you'll see that it is very similar to the inyo. Both are simply images of a red circle on a white background. The Japanese flag is known as Nisshoki, which means "sun flag," or Hinomaru, meaning "sun disc." When compared to the Japanese flag, it is no great leap to view to the inyo as a rising sun. As for the Okinawan flag, it has quite the inyo-like appearance. The inyo used by the JKA may simply symbolize the Okinawan flag, paying respect to the land where karate was born.