Tarantulas, like other 'bugs', have an hard external covering called an exoskeleton instead of an internal skeleton like humans and other mammals. In order to grow, tarantulas must shed this exoskeleton several times throughout its lifetime. A fascinating process to watch, if you happen to have five or more hours on your hands.
Here's an abbreviated version of a tarantula shedding its exoskeleton.
Molting Giant White Knee Tarantula from Peter Scott on Vimeo.