Metamorphosis is the drastic changing of a life form or organism as it transitions through different phases. This can be seen in many different creatures and in different severities. Some creatures, like the frog, start as an egg and progress through different stages, growing and adding new parts as needed. Some undergo a complete overhaul and melt down old body parts from former stages to build new parts (Butterfly, moth). Creatures can undergo little to no metamorphosis (egg -> adult organism) or something much more complicated (egg -> larva -> pupae -> adult) and can do this via different stimuli or environmental factors.
One reason creatures may have evolved this growth strategy was to have a developing form of themselves that was not confined to an egg and could "eat". If you think of maggots, or fly larva, they are able to eat food and thus give themselves a better chance of reaching adulthood while still developing. Think of them as eggs with teeth that can feed themselves.
It's also common to find that the pupal and larval stages of animals eat different foods. Caterpillars eat leaves and vegetation while butterflies focus on nectar from flowers. This means that you can have a higher amount of the organism living in an area without having to compete for different resources.
Some metamorphoses happen in very small, hardly noticeable ways. A lot of changes in creatures happen purely as they transition from a larval stage to a breeding adult. They may change in size, grow genitalia, or other methods needed as they reach an age where they can reproduce. Some caterpillars in the Arctic circle will spend years eating as a larva and upon reaching sexual maturity will metamorphose into a breeding adult that is more mobile (wings) and has a higher chance of finding mate, even though in this form their lifespans are severely cut short.