I can think of at least two reasons why it makes perfect sense.
1. The
taste of the meat of an animal is influenced by what the animal ate when alive. Thus, in a sense, the animal 'is what it ate';
2. It is to be expected that if a person eats junk or fatty foods, that they will
become fat/obese. Thus, in another sense, 'you are (fat) what you eat (fatty foods)'.