The car key is a tool used to start the Laika 601 Deluxe. The key will slide into the ignition switch, at which point the player must click and hold the left mouse button to start the car. If the car does not start, there is likely an issue with one of the Components.
It costs nothing, and is given to you by Uncle during the tutorial. Afterwards, it can be found hanging from the driver-side sun visor.