Racing fuel confers no additional benefits to non-racing cars as opposed to normal gasoline. It is not recommended to use premium or higher octane gasoline in a car that does not require it, as it is more expensive than regular unleaded gas.
Octane rating refers to the amount of pressure fuel can withstand before igniting. High performance racing cars use higher compression ratios in burning fuel. Gasoline engines are heat engines which means a higher compression ratio allows the car to extract more mechanical energy from less fuel. A lower octane fuel used in a high performance car can lead to engine knocking and less efficient fuel combustion.