When you eat other fish (but they have to be smaller than you) you grow bigger. The bigger you grow the more fish you can eat and less can eat you. Become the ruler of the ocean!
I credit the fish with the cutie marks in here to @kitkat1783. You can eat it at any time and it always gives you a 500-2000 points. Also, kitkat1783 made a remix and that has a chart that tells you how many points you need to eat certain fish. Enjoy!