I am the Kat that Walks By Itself

It's for hard soap. When you get to the point where the cake of soap has worn down to a little piece, which makes it hard to use, you put it inside the bag. So the bag gets full of little pieces of soap. Then when you wet the bag, it's like a self-soaping wash cloth.

It saves soap because it enables you to use the little pieces of soap which you might otherwise be tempted to throw away.