Cheesecloth is a gauzy cotton
cloth that's fairly coarse and loosely woven frequently used in cooking to get chunks out of fluids.
As best I understand it, it was originally used in cheesemaking. You'd have a big vat of curds and whey (basically, milk gone bad) and then you'd grab up a bunch of that with some cheesecloth and squeeze it. The whey would come out and the curds would stay in. Then squeeze a bit more so the curds get pushed together into a solid mass. Then leave it on a shelf in a cool room for a couple weeks to a couple years, possibly with more squeezing at various points to get the moisture out, and you end up with cheese.
You can typically find this in cooking stores without too much effort. It's rather unassuming looking cloth; typically has the color of unbleached cotton. Sometimes muslin can work as a replacement.
It's frequently called for to do things like strain the fat out of a soup when you don't have time to cool it or for things where a colander simply has too big of holes. (so you put a couple sheets of cheesecloth in your collander).