Quite simply, a hybrid combines at least one electric motor with a gasoline engine to move the car, and its system recaptures energy via regenerative braking. Sometimes the electric motor does all the work, sometimes it's the gas engine, and sometimes they work together. The result is less gasoline burned and, therefore, better fuel economy. Adding electric power can even boost performance in certain instances.
With all of them, electricity comes from a high-voltage battery pack (separate from the car's conventional 12-volt battery) that's replenished by capturing energy from deceleration that's typically lost to heat generated by the brakes in conventional cars. (This happens through the regenerative braking system.) Hybrids also use the gas engine to charge and maintain the battery. Car companies use different hybrid designs to accomplish different missions, ranging from maximum fuel savings to keeping the vehicle's cost as low as possible.
In this most common design, the electric motor(s) and gasoline engine are connected in a common transmission that blends the two power sources. That transmission can be an automatic, a manual, or a continuously variable transmission (CVT). One very popular hybrid transmission is a power-split CVT, which is used by the Toyota Prius and Chevrolet Volt. Transmission type and the size of the gasoline engine are the main factors that determine how a parallel hybrid will accelerate, sound, and feel. Brands that use the parallel design include Toyota, Lexus, Hyundai, Kia, Ford, Honda, Lincoln, Nissan, and Infiniti.
In this design, the electric motor(s) provides all the thrust, and there is never a physical mechanical connection between the engine and the wheels. The gasoline engine is just there to recharge the battery. This results in a driving experience that's more indicative of an electric car, with smoother, powerful acceleration. There's typically less vibration when the gasoline engine engages. However, that engagement doesn't always happen in concert with what your right foot is doing (remember, the battery is making the demands), so the engine might be revving up while the car is cruising at a steady speed. Some find this behavior disconcerting. The BMW i3 with the range extender is an example of a series hybrid.
A plug-in hybrid enhances the conventional hybrid concept with a much larger battery pack that, like an electric car's, must be fully recharged using an external electricity source—from your home, office, or public charging station. This greater amount of energy storage is like a larger gas tank: It allows for extended all-electric driving (between 15 and 55 miles depending on the model) and can significantly reduce fuel consumption. In fact, if you have a short commute and recharge nightly, you'll be running on electricity most of the time. Should you deplete the all-electric range, the car basically reverts to being a conventional parallel hybrid.