A heat engine is any type of machine and/or system that can turn heat into kinetic energy. A prime example of heat engine is the weather. When the sun shines on the Earths surface it imparts heat to the earth and in turn to the atmosphere. This heat is then used to power all of the earths weather systems from rainfall, to the water cycle, hurricanes and tornadoes.
Similarly, a machine that can turn heat into mechanical motion is also called a heat engine. The engines we would be most familiar with are the four stroke engine, two stroke engine, diesel and jet engines. While these engines do create a lot of power, they would be nowhere near as efficient as the weather systems are at converting heat into actual work.
The Stirling Engine is a very efficient heat engine. The video below shows you a perfect example of a machine turning heat into mechanical motion. This, is a heat engine -
You can learn more about the LTD (Low Temperature Differential) Stirling Engine here