They undergo metamorphosis, change of form, which is easily seen. Some insects even have different habitats as immatures than they do as adults. Mosquitoes and dragonflies fly through the air as adults living on land, but are swimmers which live under water as immatures. The changes which occur with some insects are more drastic than with others. Insects in which the young and adults look very much alike are said to have an incomplete or gradual metamorphosis.
Insects grow exclusively during the nymphal or larval periods.
They don't grow by regular gradual degrees like rabbits or dogs. The body wall will not expand like our skin to permit this. It's much like a suit of armor. In order to grow to a larger size the armor or shell must be split and shed. This process is called molting.