Like many other things, milk contains bacteria, the tiny little critters that live naturally in and on lots of things and are so small you can only see them if you use a microscope. Milk also naturally contains a kind of sugar known as “lactose.” The bacteria that live in milk get energy from this special sugar and use it to reproduce to make even more bacteria!
When the bacteria use the lactose sugars to reproduce, they change it from “lactose sugar” into “lactose acid,” which tastes sour. When this happens, the milk curdles and is no longer the smooth, tasty liquid that you're used to drinking!
While some bacteria are good, there are some that are not so good, and the kind that live in old milk can be among the ones that are better to avoid. After all, you'd probably rather have cereal be the only thing in your milk that isn't smooth and creamy!