So, it doesn't seem like anything happens. I did the tutorial, I clicked on the Koi. Then...nothing happens. My money doesn't increase, I can't buy more fish, nothing increments. My koi eats, but nothing actually happens.
You can sell the koi to earn more money when it grows to adult. It will always at least double the money you paid for it. The koi continues to grow even when the game is closed. Feeding the koi increases its growth points. There is also an Upgrade Shop ( the orange arrow on the side of the Koi Shop page) which has upgrades to increase your feed power and the koi's natural growth speed.