In mythology, koi are a symbol of strength, beauty, perseverence, luck and prosperity. They also signify a balanced and tranquil mind. In Chinese mythology there is a tale of a koi that battles its way up river and turns into a dragon.
They popularity as a tattoo is probably the same as that which makes then the most collected fish - they are very pretty.
In Japanese, the word koi just means carp. The Japanese word Nishiki is the word for Chinese coloured silk. Japanese call koi Nishikigo", or coloured carp. Koi are not goldfish. It is said that several hundred years ago farmers in the village of Yamakoshi discovered a strange red carp among the blue grey and black carp that they raised for food. By careful breeding practices, farmers began developing the colorful nishikigoi we have today.