Caterpillars or insects in general has what is called an exo skeleton. The outer layer of the body is a thick layer of chitin which is in simple terms, as kind of sugar. Since it is a dead matter, it will not grow and as the insect grows, it's outer cover becomes tight. To accommodate the increase in size, the insect makes a bigger layer of chitin underneath and when this is done, they discard the older, smaller one. It is this exoskeleton that gives the strength to the body.
In case of humans, we have an endoskeleton, or the skeleton is inside the body. And the skeleton can grow as the body grows because the bones grow along with the body, humans do not have to replace the bone as they grow. And the skin that covers the body is again made of living cells which divide and grow as the size of the body increases.
However, the outermost layer of the human skin is made of dead cells and humans too shed these dead cells all the time