When the cost to repair your car is greater than the value of the car itself, your car has been totaled.
Even though your repair cost has reached this threshold, you can still decide to keep your car and repair it. However, this will decrease the value of the vehicle, and the amount you will be paid for the total loss.
When an insurance company declares a car totaled, they inform the state’s DMV. This means the registration on the car is effectively canceled and you should remove your license plates from the car.
It will be illegal for you to drive this car. Typically, the title to the car will also get a “salvage” stamp.
To continue driving the car after repairs are done it needs to pass a DMV salvage inspection which you can learn about here. There is also a salvage inspection form with more information which you can read and fill out out here.