The koi fish in Japanese folklore represents the overcoming of obstacles, because the koi fish travels up the yellow river and when it comes to the end of the river it transforms into the dragon; thus overcoming the adversity represented by the strong river to fufill its own destiny.
The Koi is the symbol of strength and will, the will to go against odds to reach the destiny. And the Dragon is the power and ferocity. The mystery and Aura.