GFCI receptacles are designed to protect people from getting shocked. They contain sensors that measure the balance between the hot and the neutral Connections. To put it simply, it senses that there is current going somewhere it shouldn't. For example, through you! Ouch!
It is so sensitive that it will open in a few hundredths of a second, on very low fault levels. The standard fault sensitivity is set at a level that a small child can survive.
The most common faults are caused when water is present, most electrical devices that get wet could possibly cause a shock, and way very well not trip a standard circuit breaker.
One of the great things about GFCIs is that they can protect a string of receptacles. So one device could protect all of the plugs in your garage, for example.
They are required in kitchens,bathrooms, unfinished basements, within 6 feet of any basin, exteriors, and garages. The national electrical code does not require you to replace all of your plugs, in these locations, unless the device is being changed for a different reason. Personally, I recommend changing them anyway, for safety reasons.
Another use of GFCIs is to allow two prong ungrounded plugs to legally be replaced with a three prong receptacle. This is your only option if the circuit is ungrounded, and you need three prong plugs, aside from rewiring the circuit.
There are also GFCI breakers that can go in your breaker box, these cost $50 dollars and up, compared to GFCI receptacles which vary from $25 and up.
There are two buttons on the receptacles, one is the test button, which should pop when pressed, causing the plug to de-energize.
The second button is the reset button, which should turn the plug back on. If the button won't reset I recommend getting an electrician to check it out.
The plug itself could be failing, or they may be a fault that needs to be located. You can look for an obvious fault yourself first, such as an extension cord lying in a puddle.