Milk is made up of water and tiny globules of fat which have a tendency to stick together and form clumps. When left alone, the fat in a glass of milk taken directly from a cow will separate from the rest of the milk because all of the fat globules will clump together. When cold, this can happen in less than one hour!

You may wonder why the milk we buy in stores does not do this. In fact, the milk that we buy is stores is "homogenized". What this means is that the milk has gone through a process to make all of the fat globules very small and very nearly the same size. This slows down the clumping process and keeps the fat from separating. I think the reason is that big globules rise faster than small globules so that in raw milk the big globules will rise quickly and collect all of the smaller globules as it moves up. Making all the globules tiny and the same size (so that no globule rises too much faster than any other) slows this process down.

Now on to your question: Shaking tends to bring the globules much closer together than they normally would go. When two globules collide, they tend to clump and pretty soon you have a bunch of big clumps of fat which rise to the top. Butter itself is nothing more than milk fat and salt, with tiny (too small to see) droplets of water.

"Emulsion" comes to mind when I read your question. I did a search on www.google.com for: butter churning and found this website: here

This site says that butter is a water-in-oil emulsion, comprised of >80% milk fat, but also containing water in the form of tiny droplets, perhaps some milk solids-not-fat. The fat globules of cream seem to get broken down into smaller globules by shaking, and and little watery spheres get trapped in the fat.

I found another site which says that butter is made up of fat, protein, and water. They form an emulsion, which means that you have a mixture of substances that usually don't mix (oil and water).