In Japan Kois bring good fortune or good luck. They also are associated with perseverance in adversity and strength of purpose. In Buddhism they symbolise courage. The fish are considered to be symbolic of advancement materially and spiritually.
The colours of the fish have a meaning as follows:
Bekko: The translation of the name is “tortoise shell”, and these fish can be red, yellow, or white.
Kohaku: The two major colors, white and red, which is the very meaning of their name. These color are know to be symbolic of career success.
Kuchibeni: The red and white color symbolize love
Yamabuki Koi: The gold fish represents (of course) gold, wealth and prosperity.