Fuel is vital in Car Town, and serves as the Energy meter that you will find in most other Facebook Games. You use Fuel up by racing against other drivers, either in street races or on the High Stakes Track (currently closed). The other races in Car Town do not use it up.
If you want to purchase more fuel using Points/Facebook Credits, click on Edit Garage, you will then see the following options for adding more Fuel, without having to wait for it to recharge.
3 Gallons of Fuel - 2 Points/Facebook Credits
7 Gallons of Fuel - 5 Points/Facebook Credits
12 Gallons of Fuel - 8 Points/Facebook Credits