Hybrids come in different flavors, ranging from basic MPG savings all the way up to no gas-consuming electric vehicles (EVs).
A "mild hybrid" was popular in the early 2000's for manufacturers who wanted to slap a "hybrid" sticker on their cars, but didn't want to go crazy with the technology. These vehicles typically have a "stop-start" mechanism which turns off the engine when the car isn't moving in an effort to save gas. Fuel savings are usually pretty minimal, but they do have an effect.
A pure or full hybrid are very fuel efficient. They use the same technologies as mild hybrids and can navigate between multiple modes of operation -- run purely on gas for more power, a mix of gas and electric for everyday use, and pure electric for cruising.
A plug-in hybrid (PHEV) typically have larger batteries than pure hybrids and can be plugged into an outlet to increase their on-board supply of electricity.