In many states if you want to keep you car that an insurance company has declared to be a total loss you can buy it back from the insurance company.
In the auto insurance business, a motor vehicle is termed a "total loss" if the either the car cannot be repaired or if the cost to fix the vehicle is near or more than the actual cash value of the automobile. Some people buy back this totaled vehicle (and get a salvaged title) so that they can repair the vehicle and continue to drive it. In some states once the car is repaired it can then get a rebuilt title on it.
Typically after the settlement is paid for a vehicle that is found to be a total loss the damaged car goes to an auction or salvage yard, where it is typically auctioned to the highest bidder and used for parts. The insurance company keeps the proceeds of this sale.
If you want to keep your damaged vehicle, some insurance companies will forgo the auction process and turn the car over to you (usually in cases where the car is over 10 years old). They will still have to pay you the actual cash value of the car, minus any amount the car would have brought at auction (salvage value), this is buying the vehicle back. At that point, it is up to you to pay for the necessary repairs. If your insurer allows you to do this, you will have to inform your insurer right away if you want your car back. Once it goes to the salvage yard, you will have little chance of getting it back, since only licensed auto salvagers are normally allowed to attend these auctions.
Even if your insurer allows you to buy back the car, it may not be worth the time and expense to get it back on the road if your state has a number of special requirements you must satisfy (e.g., buying a salvage title or having the car inspected by the state police after it's been repaired). Also, some insurance companies will not insure vehicle with a salvage title so it may difficult to find insurance for the vehicle it now that it has a salvage title on it.