A private (or "cherished") plate replaces the standard age-identifying plate with a personalised combination that doesn't reveal when the car was registered.
What this means for a buyer: you genuinely can't tell a car's age just by looking at a private plate the way you can with a standard one. But swapping the visible plate doesn't change the vehicle's underlying registration record - the true first registration date is still held against the car, it's just not displayed on the plate itself.