GPS stands for the Global Positioning System, which is a navigational system based on 24 different satellites originally intended for military use. These satellites where placed into orbit by the U.S. Department of Defense; however, in the 1980s, the government made the system available for regular civilians to use.

Each GPS satellite transmits a signal to Earth indicating the current time along with its current position in the sky.  GPS devices take this information and use triangulation to calculate the user's exact location. Basically, the GPS receiver compares the time from the signal to the current time, takes the difference of these two times, and uses that to calculate the distance between the device and the satellite.

It does this for 3-4 or more satellites. This way, the device is able to determine, within a few meters, the exact location of the device and then display the coordinates on the device's map. If it's connected to 3 satellites, it can determine latitude and longitude. If it's connected to 4 or more, it can also determine altitude. 

Once it knows the position of the device, it can then compare positions of where the device was in the past. This is used to determine speed, bearing, trip distance, etc.  For example, a mountain biker at the top of the mountain can find out what their average speed was when they reach the bottom based on how long it took and the distance traveled.  They can also determine the elevation change between the top and bottom.  Many devices also allow the user to upload their trip so that they can see it on an interactive map.

GPS works around the world, 24 hours a day, and it also works during any type of weather conditions.  There are no subscription fees to use the system, although vendors may have subscriptions for add-on services such as cloud storage to keep a log of many different trips taken.