"Quarter panels" refers to the metal parts on the sides of a vehicle, specifically between the rear window and the trunk or rear bumper. They are responsible for protecting the rear wheel area and add structure to the car's body. Full definition
The facelift left only the doors, the roof, and the rear quarter panels on the estate the same as the original model. (en.m.wikipedia.org)
The right front tire took the majority of the hit, with damage largely confined to the right front quarter panel and the right front door. (mechanics.stackexchange.com)
Some bubbling is present on the passenger - side quarter panel. (bringatrailer.com)