As Kathryn explained, when milk is left on its own, fat globules collect together and rise to the surface of the liquid to form that delicious layer of cream. Homogenization prevents the fat globules from clumping and keeps the fat dispersed in a kind of emulsion throughout the milk.
To do this, hot milk is pumped through small screens at very high pressure. This breaks the fat into smaller and smaller globules and also strips away their protective membrane. Casein, an emulsifying agent naturally present in milk, adheres to the bare surface of the fat. The casein both weighs the fat down (preventing it from rising to the surface) and keeps the fat molecules from collecting together.
Homogenization makes for a creamier milk since the smaller and more numerous fat globules coat the tongue more evenly. On the downside, homogenized milk usually tastes bland when compared to non-homogenized milk because the process also disrupts flavor molecules in the milk.
While homogenization and pasteurization usually go hand-in-hand, this isn't strictly necessary and likely has more to do with consumer demand. We'll talk more about pasteurization next week!