A car engine is generally an internal combustion engine. This means that it combines fuel and air and combusts it together in a chamber to get it running. This combustion creates a force which in turn moves the pistons which gives the car the power it needs to move once it is applied through the gearbox, driveshaft and down to the wheel. These engines come in all different sizes and capacities. For example you can have a petrol engine having 3 cylinders to a petrol engine that has 12 cylinders, known as a V12. They would have very different properties and outputs but would still be working on the same basic principles of an internal combustion engine. The 3 cylinder engine would be economical but have a small amount of power making it ideal for small every day cars. You then have the V12 engine which would be extremely powerful and would be used in high end sports cars but they would cost a considerable amount to run. You then also have diesel engines which again work slightly different and are also very popular in commercial and plant vehicles such as vans, lorries and forklifts etc. A diesel engine is known for its good economy and also its durability, as they are known to do significantly more miles than a petrol engine.
Another engine that is less common is known as a wankel rotary engine. Rather than having pistons to combust and pressurise the gases it uses a triangular rotar that spins and completes the same phases as an internal combustion engine. It is known for being used in Mazda's RX-7 and RX-8.