In biology, "animal" refers to the entire animal kingdom, which is, roughly, anything that is not a plant or a microorganism.
Insects are a kind of animal. So are birds, fish, and worms.
In ordinary speech, "animals" often means "mammals." Mammals usually sweat, have hair on their bodies, bear their young alive (instead of laying eggs), and feed their young with milk. Pigs are mammals. So are dogs, cats, elephants, mice, and a category called "primates."
Apes are primates. Gorillas, monkeys, and chimpanzees are primates. Human beings are primates.
Whether human beings are "just" animals, or whether they have a fundamental difference from all other animals, has been argued for centuries.
Mark Twain had a funny, but wise statement. He said "Man is the only animal that blushes--or needs to."