Fire up your electric beater and whiz it around in a bowl of whipping cream.
In a short while, you'll have mounds of a delicate, frothy foam, suitable for topping fresh berries or pies.
Now take that same beater and whiz it around a bowl of skimmed milk. You might get some temporary bubbles, or even a little foam, but it won't ever have the structure of whipped cream.
Whipped cream is a suspension of tiny bubbles in the liquid cream. These bubbles are locked in place by protein molecules and fat. Without that fat and protein, those bubbles would never stay in place. They'd quickly bubble to the top, and the cream would remain a liquid.
How does this work?
Your electric beater fills the cream with tiny bubbles, and some of the cream's protein molecules are caught in the thin walls of the bubbles. Surrounded by liquid, these protein molecules are ordinarily separate, but the presence of all that air causes the individual proteins to stretch out and lock together in a process called coagulation. Whipping cream also has a lot of fat globules in it. Nearly twenty percent of it's overall volume is fat. These globules rupture along the bubble walls, and the fat helps the proteins stick together.
Without this teamwork between fat and protein, cream wouldn't whip into a stable foam.
Milk whips poorly because there's much less fat in it. The milk proteins begin to coagulate, and try to lock the bubbles in place, but without fat to hold it all together, those bubbles bubble up and away, leaving behind liquid milk.