A tarantula grows only by ecdysis. The spider stops feeding, lies on its back for hours, and splits the old carapace, drawing itself out of a cuticle that is continuous with structures well inside the body.
What comes away is not simply a shell. The cast skin includes the cuticular lining of the fangs, the book lungs, the foregut and, in mature females, part of the reproductive tract. New fangs are pale and soft, and the animal cannot safely subdue prey until they harden, which usually takes several days. Legs lost earlier can be regrown across successive moults, at first shorter than their neighbours.
The name is a borrowed one. It comes from Taranto in southern Italy and originally referred to Lycosa tarantula, a European wolf spider blamed for a dancing hysteria called tarantism. The large hairy spiders of the Americas inherited the word from travellers, not from any shared biology.