The chemically chopped up version of the big protein molecule, collagen. It is often derived from fish or bovine sources and works as a nice moisturizer and humectant that helps the skin to hold onto water.
To understand a bit more what Hydrolyzed Collagen is, you have to know that proteins are large chains of amino acids connected with so-called peptide bonds. These bonds can be broken up when a water molecule is added and the resulting thing is a mix of shorter length amino acids, also called peptides. So Hydrolyzed Collagen is not really collagen, it is rather an undefined and varying mix of largish peptides. Based on a manufacturer's data, the whole, soluble collagen has an average molecular weight of 300 000 Da, while this chopped up mixture has an average MW of 12 000 Da (still pretty big).
The main thing of these largish peptides is to act as water-binding agents, and to make the skin nice and smooth (aka emollient). Hydrolyzed Collagen is also often used in cleansers as it can make harsh surfactants milder and in hair conditioners as it improves the flexibility and manageability of hair.
If you wanna know more about collagen in cosmetics, we have a shiny explanation about soluble collagen here >>