Whipping cream is a suspension of fat globules and water-based liquid. When you start to whip it, air is incorporated into the cream while the mechanical action of the whisk actually strips away the outer surface of the fat globules. The combination of these two things is what turns cream from a liquid into a solid.
If you keep whipping the cream beyond the point of wanting to put it on your ice cream, structure eventually becomes so destabilized that the separate fat globules start to form together into a solid mass. At first you'll just see tiny "seed" grains, and then larger and larger masses will form. This mass - butter! - forces out the watery liquid, and the original suspension of fat and liquid is broken. Drain off the liquid (or save it for baking) and you have fresh butter!
How quickly and effectively this separation happens depends on the fat content of the original cream. If your intention is to make butter, try to find a cream that is at least 35% fat, and ideally, unhomogenized. Creams with less fat content will take longer and produce less butter.
Have you ever made butter at home, intentionally or unintentionally?!