Monarchs, like other butterflies and moths, undergo complete metamorphosis, meaning that they have an egg, larva (caterpillar), pupa (chrysalis), and adult stage. The egg and caterpillar stages occur only on species of milkweed (genus Asclepias) whereas adults survive by nectaring on a variety of flowering plants.
Female monarchs only lay eggs on milkweed plants since monarch caterpillars only eat milkweed. The milkweed plant provides both food and shelter for a caterpillar for approximately two weeks (dependent on temperature), while it eats almost constantly, pausing only to shed its skin. The period between each shedding of the skin, or molt, is called an instar. Monarchs have five larval instars and grow to almost 2000 times their original mass.
A late fifth instar monarch will generally crawl away from the milkweed plant it was feeding on to find a secure location where it forms a silk pad and hangs upside down in a J shape before shedding its skin one last time to expose the bright green chrysalis. In 8 to 15 days, an adult emerges, pumps fluid to its wings to give them shape, and spends several hours drying before it is ready to venture off to find nectar or a mate.
To watch a timelapse of a monarch emerging from its chrysalis, watch this video.