Homogenised milk is processed milk, through heat and other forces, where the cream ends up blended in the milk, making a smoother milk. When I grew up, our milk was non homogenised and had a cream layer on top of the milk. This was all I knew and as a kid, I thought this was just luxury. I would actually get excited about a new bottle of milk so that I could put the cream layer on my cereal. You can still buy non homogenised milk but it is definitely hard to come by.
I make cheese at home fairly regularly and this always call for homogenised milk where the cream is already sitting within the milk.
This, from what I understand, is a process where they break down the fat molecules by through a shaking process. I also heard that since the molecules are easier to digest that they enter the blood stream and line the arteries thus aiding the increase to heart disease. However I have not found in evidence from the FDA to support this.
I wonder what shaking does to the milk. I know with human milk (breast milk, though I think calling it human milk makes more sense since we don't call cow's milk "udder milk") you are not supposed to shake it because that denatures the proteins, making it not as nutritious (you stir it gently instead).
Milk that's had the cream, which would normally rise to the top, stirred back through it using a machine. When I was a kid we used to get non homogenised milk delivered which had a skin on the top. I always thought it was disgusting but older people tell me that they preferred it that way because you knew the milk was fresh.
Milk is homogenised by mixing a lot of it together, then forcing it at high pressure through small holes so that the cream is distributed evenly through the milk. I've been able to find a brand that still produces unhomogenised milk and personally, I like it better because I like the creamy texture in my tea. My kids hate it though, because of the cream on top, which seems weird to them, so we get both kinds.