Caterpillars have a fresh new exoskeleton underneath the 'too small' one that they shed. Typically, they simply stop feeding (temperarily) and begin to take in an excess of air through the spiracles (breathing tubes) along their sides. This helps them expand, splitting the old skin and allowing them to get rid of it.

On average, most caterpillars go through 4 or 5 molts before they are finished growing. The process can take quite some time to complete (up to 24 hours or so!) and they are quite vulnerable in this period. I guess SO! Bare naked for all the world to see. ;-)

Underneath that old skin, the new one needs a while to harden properly but the caterpillars are good to go for a few more days of eating and eating and growing in between those molts. (Those periods in between are called the instars, but you already know that, I'll bet.)

The 'new' skin is also sort of 'wet' and many caterpillars will eat their molted exuviae. In the final molt, what remains is the 'head capsule' of the caterpillar, which you often find either precariously attached to the pupa (chrysalis) or fallen on the ground resembling a giant poop. My Kindergartners LOVE spotting the head capsule.