Hi. When a standard hybrid car is driving over about 25 mph, the gasoline engine is being used to propel the car. As it is doing so it is also working just as a generator does (like the kind you would use to run electricity in a home if your power went out or to power a cabin in the woods or on a boat.) The electricity that is produced from the engine as you are driving is stored in a large battery pack. When the car is driving slower than 25 mph or so (on average) then the gasoline motor automatically shuts off and the power from the batteries is sent to an electric motor (or motors), so no gas is being burned. Gasoline currently has a lot more stored energy than electricity does, so the car needs that power to move it at freeway speeds.
On any hybrid currently on the market you don't need to plug it in, because all the electricity comes from the gas engine as you are driving. Another option coming up sometime soon is the plug-in hybrid, in which a larger battery pack is plugged in when it isn't used, increasing range and power available for the electric motor. Some do-it-yourselfers who have done this to their own hybrids (voiding the warranty, though) have reported going from about 50+ mph up to 99 mph or so.
http://auto.howstuffworks.com/hybrid-car.htm has a great visual description.