Incomplete metamorphosis, hemimetabolism, is one of the forms that an insect's life cycle can take. In incomplete metamorphosis, a newly hatched insect looks much like a smaller version of an adult of its species. It is called a nymph.
A nymph never goes through a pupal stage, never radically changes in the way that caterpillars do as they become butterflies. When it reaches the imago (adult) stage, a nymph may acquire the wings that it lacked as an immature insect. It may breathe differently, and its coloration and form may change slightly. However, it will largely go on as it began. There is never an utter transformation.
Complete metamorphosis, holometabolism, occurs when there are two stages between egg and adult. The creature that comes out of the egg is a larva, which does not appear to resemble the adult form in any way. It eats and grows, and then enters the pupal stage, in which it utterly transforms, and becomes an adult, an imago.
All insects begin as eggs. They may have been placed in water, hidden inside plant stems or bark, or even, as some Stick Insect eggs are, have been dropped in ants' nests. Some insect mothers secrete organic glue from their abdomens and fasten their eggs in crevices or beneath leaves.
When the nymphs emerge, they are already very close to their adult form. They do still have to acquire some adult characteristics. They also have to survive, to eat, and to grow.
As they grow, they must periodically molt. Insects have hard inflexible exoskeletons. In effect, their bone structure is on the outside, encasing them. Therefore, even though an insect grows, the growth cannot be seen, because the insect's body is crumpled up and confined in a hard resistant shell that stays the same size.
Eventually, the insect will crack out of its exoskeleton, and suddenly increase in size. A new exoskeleton will quickly harden to protect the nymph. Most nymphs molt many times before they reach adult size.
A nymph is different from an adult in subtle but important ways. In winged species, a nymph cannot yet fly. Its wings are useless stubs at birth and do not become operative until the nymph is grown. In many of the species that deposit their eggs in water, such as dragonflies, a nymph cannot breathe air, but takes its oxygen from the water with gills. When a dragonfly leaves the water, it must begin to breathe air as it first moves its wings.
When an insect finally reaches maturity, it cracks out of its last nymph exoskeleton, and likely begins to look for a mate. If the pair successfully breeds, the cycle will begin again.
The term incomplete metamorphosis describes an insect life cycle in which the nymph is very much like the imago. Immature insects of this type are essentially smaller copies of adults, though they lack certain adult characteristics and behaviors.