Global Positioning Satellites
Satellites provide the backbone of the Global Positioning System (GPS). The Earth is literally surrounded by these GPS satellites. There are 24 of them floating around out there. Each one resides in its own orbit. These orbits are tracked from stations on the ground that constantly relay back to the satellite its exact location.
These precisely positioned satellites send out their own periodic signal. Each signal carries with it a time stamp that tells the exact moment it left the satellite as well as its exact position. This signal is beamed to the Earth where it is picked up by any GPS device that happens to be in the area. The device will know exactly how long this signal took to get to the device. Every fraction of a second the signal takes to reach the GPS device tells the device that the device itself is that much farther from the point corresponding with the particular satellite.
The time the signal takes is converted to distance by knowing the speed of the radio wave that sent it. If you had a map of the Earth and knew where the satellite's point of reference on Earth was you could draw a circle on the map around the point and know that you had to be somewhere on this circular line. (You would have to use a bit of trigonometry to calculate the size of the circle as, you understand, the line directly to the satellite is the hypotenuse of a triangle while the distance above the earth is another side. You would know the angle off the horizon of the satellite and this would be enough to give you the calculation for the length of the third leg.)
But this only gives you a circle. You are going to need more points and more satellites to get an exact fix.