It's the official change of your registered residence in the anagrafe. You file it at your new comune (or online through ANPR) when you move address. A vigile may visit to confirm you actually live there.
Many things depend on your current residenza: tax rates, GP assignment, ID card, prima casa rules, school catchment. Forgetting to update can mean lost benefits and bureaucratic headaches.
"After Mariusz signed a new lease in Frosinone, he filed the cambio di residenza online through ANPR using his SPID. A few weeks later a local officer rang the bell and ticked a checklist."
Your old comune is automatically informed. You don't need to deregister there separately. The new comune handles the transfer in the background.
Official source
ANPR
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