Flesh is the part of a body that's made of muscles and fat. If you grab the flesh of your little brother's arm to keep him from running into the street, you're holding the soft part of his arm.
We often use the word flesh to talk about the tissues of an animal's body — in other words, the fat and muscle that most humans consider to be food, or meat. But you'll also hear people say "flesh and bone" or "flesh and blood" when they're describing the physical parts of a human. The Old English root is flæsc, "flesh or meat."