What owner-retained salvage means
Instead of surrendering the vehicle to the insurer, you keep it — and the insurer typically deducts the vehicle's salvage (scrap/parts) value from your settlement, since they're not taking possession of it. You receive a reduced payout, and you keep the car.
Title branding
A vehicle declared a total loss and retained by its owner generally receives a branded title — commonly called a salvage title, and later a rebuilt or reconstructed title once it passes any required inspection. A branded title is permanent and follows the vehicle through future sales; it typically affects resale value and, for some vehicles, insurability.
Getting it back on the road
Depending on where you live, putting a salvage-titled vehicle back into regular use may require a formal inspection (sometimes focused on structural or safety systems), specific paperwork to move from a salvage to a rebuilt title, and in some cases limitations on what can be done with the vehicle in the meantime.
Why this varies so much by state
Salvage-title triggers, inspection requirements, and rebuild processes are set at the state level, and they differ meaningfully from state to state — there is no single national rule. Rather than guess at your state's specific requirements, check the dedicated reference below.