Hybrid Engines are typically described as engines with two power sources. The most common today is a hybrid gas-electric engine that combines the low pollution output of an electric engine, with the high power output of a gas engine.
There are as many gas-electric engines as there are hybrid cars. Each engine is designed to allow the gas engine and the electric engine to connect to the drive train to power the engine.
The gas engine and the brakes are used to recharge the battery for the electric engine eliminating the need to plug in overnight, as is necessary for a plug in electric only engine. When braking, some of the energy being expended to stop a car is collected by the regenerative brakes in an electric engine.
Typically, in a full hybrid, the electric engine takes control when the car is cruising, at stop, or when slowly accelerating. When extra power is needed, the gas engine kicks in to give the acceleration expected from today's cars. By allowing the electric engine to take over, hybrids are able to get higher mpg than their sister cars with gas only engines. But since most of the energy is collected/saved when the car is stopped or in braking, hybrid cars tend to get better mileage in city driving. Which is opposite what gas only cars should expect, as gas engines are most efficient at high speeds (highway).
When comparing hybrid cars to plug-ins, hybrid engines have not only eliminated the need for plugging in, they have also increased the range that is possible.