Certain groups of insects completely change appearance when they change from larva to adult insect. The transition often takes place inside a protective covering called a cocoon or a chrysalis.
The cocoon with the developing insect inside is called the pupa, as well as the phase of life of the insect. During the pupa-stage the insect is unable to move. In fact a lot of the organs, muscles and other structures or bodyparts of the larva are completely remodeled before the adult insect emerges from the cocoon. The most obvious evidence for this is the orientation by which a butterfly emerges from the cocoon. Its the other way around than the caterpillar was when it entered the pupa stage.
Note: Not all insects go through a pupa stage. Quite a few (eg grasshoppers) just have a simple moulting between the last larval stage and the sexualy active adult stage