Like many popular elements from oriental tattoo design such as lotus flowers and dragons, koi fish tattoo designs have permeated into Western tattoo culture - despite the negative connotations tattoos have in Japan (tattoos were at one time illegal and are often associated with the Japanese Mafia).The Japanese tattoo artists who first started inking kois were inspired by an oriental legend that said if a koi carp could swim upstream the river to Dragon Gate on the Yellow River, the koi would be rewarded by being transformed into a dragon. 
If the koi was caught, it would lie still one the chopping board and accept death honorably - like a Samurai warrior. For this reason, koi tattoo designs represent courage, perseverance and tenacity through life's difficulties, aswell as honor in failure.
A koi swimming downstream usually means the tattooee has overcome their difficulties, whereas a koi swimming upstream implies that the tattooee is still struggling through hardship.