It depends on the type of animal, but if, for example, you're talking about one lower on the energy pyramid (like a chicken, for example) then this is because of the energy distribution. When an animal consumes something else, it absorbs about 10 percent of the energy of that creature.
So, lets say a plant has 1000 units of energy. Then a bug comes along, and eats the plant, absorbing 100 units (10 percent) of that energy. Then, a chicken eats the bug, absorbing only 10 units of that energy. Finally, a human eats the chicken, getting only 1 unit of the original energy.
The reason that something like a bug has to eat less than a human, is because it gets more energy directly from the plant.