What makes the hair remover Nair work?

The ingredients of Nair are: Water, Mineral Oil, Calcium Hydroxidem, Urea, Potassium Thioglycolate, Cetearyl Alcohol, Ceteareth-20, Sodium Hydroxide, Cocoa (Theobroma Cacao) Butter, Fragrance, Tocopherol (Vitamin #), and D&C Yellow No. 8.

Ok, now it's been a while since I've had chem class, but if memory serves, Calcium Hydroxidem and Sodium Hydroxide are not to be toyed with. Offhand, I imagine it probably oxidizes the hair and dissolves it that way. I don't know the chemical makeup of hair, and I forget exactly what the formula for Calcium Hydroxidem is, so I can't write up a chemical formula for you. I hope this was helpful, all the same?