Moulting

Moulting (or molting) is the manner in which an animal routinely casts off part of its body (usually the outer layer or covering) at particular times of year, or at specific points in its life cycle. Moulting is also known as sloughing, shedding, or for some species, ecdysis.
Moulting can involve the epidermis (skin), and hair, fur, wool, or other external layer. In some species, other body parts may be shed, for example, wings in some insects. Examples include old feathers in birds, old hairs in mammals (especially dogs and other canidae), old skin in reptiles, and the entire exoskeleton in arthropods.
Ecdysis.
In arthropods, such as insects, arachnids and crustaceans, moulting is the shedding of the exoskeleton (or shell). 
This process of moulting is called ecdysis. It is the defining feature of a whole group of invertebrates, the clade Ecdysozoa. This group includes the arthropods, nematodes, velvet worms, horsehair worms, rotifers, tardigrades and Cephalorhyncha. Since the cuticles of these animals often forms an inelastic exoskeleton, it is shed during growth and a new, larger covering is formed. Amongst fossils, trilobites and eurypterida used ecdysis. 
Ecdysis is part of the whole process of metamorphosis. The different stages (called 'instars') and the development of new 'apparatus' (such as sense organs) is necessary as the creature moves from one form to another. The new exoskeleton is initially soft but hardens after the moulting of the old exoskeleton.