An insectivore is an animal that eats only or mainly insects. If chocolate-covered crickets are your thing, then go ahead and call yourself an insectivore (and good luck finding a date).
A carnivore is an animal that eats other animals, and an insectivore is a more specific type of carnivore: one whose diet is mainly insects. Insectivores include many lizards, frogs, and spiders. A spider catching a bug in a web and a frog catching a fly with its tongue are two examples of insectivore behavior. Since there are millions of insects in the world, being an insectivore is a pretty good deal.