The Motor Generator Unit - Heat (usually abbreviated as MGU-H) is a component of a hybrid-electric internal combustion engine. The unit is an evolved component of a turbocharger, where the exhaust gasses (the "heat" part of the name) are used to also generate electricity, and the unit also functions as a motor.
The fundamental action of an internal combustion engine is gas expansion, by the explosive combustion of the air/fuel mixture within the cylinder by the spark plug. While the majority of the energy derived is utilized by pushing the piston towards the crankshaft, a sizeable amount is turned into heat in the exhaust gasses, and is simply expelled out through the exhaust piping.
The turbocharger increases the efficiency of the motor unit by using the force of the heat-induced gas expansion to drive a turbine, compressing the incoming air before combining it with the fuel and igniting the mixture. The MGU-H unit further increases efficiency by a direct link with the turbine, to generate electrical power.
At lower engine revolutions, the MGU-H acts as a motor, driving the turbocharging system to alleviate throttle lag. But when the turbocharger and engine reach thresholds, the MGU-H becomes a generator, using the exhaust to generate electricity for the batteries of the drive assist system. The net effect is both greater power and fuel efficiency, and is regarded as a significant development in automotive technology.
In a modern system, the exhaust turbine and inlet compressor still act as a strictly mechanical turbocharger, and does provide increased power in case of electrical failure.