Metamorphosis, otherwise known as shape shifting, is a transformation in form by the dreamer into another person or animal/fictional creature. It is an example of dream control.
A dreamer often undergoes metamorphosis to gain an ability that is more inclined towards the morphed form; e.g. one can morph into a bird to fly, a whale to swim, or morph into another character to disguise one's true identity.
Often upon metamorphosis the dreamer can actually sense a change in form, e.g. if morphing to a quadriped, he can feel four legs as opposed to two legs and two arms.
A lucid dreamer may also just transform for the heck of it, to see what it feels like, or if they have some sort of liking for whatever they are morphing into. Usually these people focus on what the form feels like, and the experience can be unforgettable (figuratively). The dreamer may morph into a fictional creature as well as a real animal, and the only real limit is their imagination. The creature does not even have to be known to anyone else, as long as they know what it is they can become it. Some people report morphing into non-animal forms, like the ocean.
Many find it good to make an excuse (a machine or person) with the ability to change your form.