What Are The 4 Stages In The Life Cycle Of An Insect?

When an insect lays eggs, they do not just hatch and grow into a similar but larger insect. In fact, insects undergo complete or partial metamorphosis to become an adult insect. The insects that undergo partial metamorphosis are known as hemimetabolous insects and these have three stages in their life cycle (egg, nymph, adult).
We are interested in the holometabolous insects, those which undergo complete metamorphosis during their life cycle. A very common example of such type of insects is the butterfly. They have four stages in their life cycle. The stages are:

Egg -> larva -> pupa -> adult

The adult that emerges from the pupa are nothing like the larva. Again, think butterflies. Caterpillars are prickly worm like creatures and nothing like the beautiful winged insect that emerges from the pupa.
When an egg hatches, a larva comes out. Larvae eat a lot. Let's carry on the example of the caterpillar. So, when a butterfly's egg hatches, out comes a caterpillar. Always hungry, it eats a lot. When it is all fed, it finds a safe spot and settles there as the pupa. There, it molts its skin and produces a pupal skin which surrounds it to form a cacoon. The caterpillar does not eat or move at this stage. It then digests most of its body and then then a new body is produced which resembles that of a butterfly. When the growth is complete, it comes out of its cacoon as a butterfly.
This butterfly is an adult and can mate and produce more eggs, which would hatch into many larvae, and the cycle continues.