A real cellular process, and a popular buzzword that's outrun some of the evidence behind it.
Autophagy — literally "self-eating" — is a genuine, well-documented cellular process where cells break down and recycle damaged components. It's a normal, ongoing part of cellular maintenance, not something that only switches on during fasting.
Much of the specific, precise messaging around fasting and autophagy — like claims that a specific number of hours of fasting triggers a specific autophagy boost — is extrapolated from animal studies (often using far longer relative fasting periods than intermittent fasting protocols use in humans) rather than firmly established at those exact timeframes in people.
Fasting periods do appear to increase autophagy activity in human studies to some degree, and this is one of the proposed mechanisms behind some of intermittent fasting's studied metabolic benefits — but the precise dose-response relationship in humans (how many hours, how much benefit) is considerably less settled than popular content often implies.
If cellular "self-cleanup" appeals to you, general good sleep, exercise and avoiding constant snacking all support the same underlying processes — fasting isn't the only lever, even if it's the most talked about.