Stirling Cycle engines like their cousins the Steam Engine and Internal Combustion Engines are heat engines in that they use heat to produce working power. They are different in that they do not directly burn fuel to produce that working power. The Stirling engine usually is a two piston arrangement, or more correctly one piston and one displacer. The engine usually consists of a pair of cylinders, one small and one large which are interconnected. The power piston is in the small cylinder and is mechanically linked to the displacer in the large cylinder. The engine works by first heating the air trapped within the power cylinder expanding it forcing the power piston out. The trapped air transfers into the displacer cylinder where it is cooled and contracts, as it contracts the displacer piston and power piston are sucked back in. The air transfers back into the heated chamber where the process starts again. Note that the key is not the heat, the key is the temperature differential between the two cylinders, you can chill the displacer side of the engine and have it work just as well as if you heated the power side. For more detail see How Stirling Engines Operate.
In the last century Stirling cycle engines predominantly found fame as quiet pumping engines for houses. With a small amount of coal they could keep water pumping all day. More recently the world has been turning to Stirling cycle for a more efficient way to power generators and cars. There are some engines in commercial production at present capable of doing this. Of course like the electric car, the Stirling car will be a slow accelerating beast.
Stirling engines are being tested by NASA (USA Space Agency) for use in space using only solar energy to directly power moving machinery.