The biological term for a snake shedding its old skin is ecdysis.
As a snake grows, its outer skin does not expand indefinitely. A new layer develops beneath the old one, and the snake eventually loosens and removes the older covering, often by rubbing against rough surfaces. The shed skin is commonly called a snakeskin or slough.
Before shedding, many snakes become less active and their eyes may look cloudy because the old outer eye covering separates from the new one. After the process is complete, the snake’s colours may appear brighter.
Ecdysis also occurs in other arthropods and reptiles, so it is not exclusive to snakes. Brumation, by contrast, is a period of reduced winter activity and is unrelated to skin shedding.