The unfancy name for it is lye. It’s a solid white stuff that’s very alkaline and used in small amounts to adjust the pH of the product and make it just right.
For example, in case of AHA or BHA exfoliants, the right pH is super-duper important, and pH adjusters like sodium hydroxide are needed.
BTW, lye is not something new. It was already used by ancient Egyptians to help oil and fat magically turn into something else. Can you guess what? Yes, it’s soap. It still often shows up in the ingredient list of soaps and other cleansers.
Sodium hydroxide in itself is a potent skin irritant, but once it's reacted (as it is usually in skin care products, like exfoliants) it is totally harmless.