"Curds and whey" refers to the lumps and liquid that are found in cottage cheese. When "Miss Muffet" was eating her curds and whey in the nursery rhyme, she was actually eating watery cottage cheese.
Cottage cheese is made from skim milk through the process of adding a chemical known as rennin, which is an enzyme found in the stomach of calves and is also found in rennet. When rennin is added to the skim milk, some of the proteins clump together, creating the curds in the cottage cheese. The remaining liquid, the whey, is simply the left-over skim milk protein that refused to clump, and it is often drained off, leaving the curds.