Imagine you’re completely lost. You wake up in a strange hotel room one morning with no idea at all where you are. You go downstairs and ask the hotel receptionist, "Where am I?" “I can’t say” he says, “but I will tell you you’re 593 miles/ 955 kilometres from Copenhagen.” You now know you’re somewhere on a circle round Copenhagen with a radius of 593 miles/ 955 kilometres. You stroll into town and, stopping off for a coffee, ask the waitress where you are. “375 miles/ 604 kilometres from Paris" she says and walks away. You then notice the table napkins. As luck would have it, they are perfect detailed maps of Europe! You take one, pull out your handy compass-and-ruler accessory set and draw two circles. So: You now know you must be at one of the two points where the circles intersect. The only two points both 593 miles/ 955 kilometres from Copenhagen and 375 miles/ 604 kilometres from Paris. Back on the street an old man calls you over. He tells you that you are 317 miles/ 510 kilometres from Prague. You whip out your napkin and compass and draw another circle. You now know exactly where you are: Frankfurt!
3-D trilateration is basically the same idea as 2-D trilateration. You just need to imagine the 2-D example above, but with 3 spheres instead of 3 circles. Let’s say you know you’re 10 miles/ kilometres from satellite A. This means you could be anywhere on the surface of a huge, imaginary sphere with a 10 mile/ kilometre radius. But if you also know you’re 15 miles/ kilometres from satellite B, you can overlap the first sphere with this second sphere with a 15 mile/ kilometre radius. The two spheres will intersect in a perfect 2-D circle. And if you also know you’re 8 miles/ kilometres from a third satellite, when you make this third sphere, you will find it intersects with the circle at two points (just like the two-circle diagram in the 2-D example). But you also have a 4th sphere handy: the Earth itself. Only one of the two intersecting points you’ve just identified will actually be on the Earth’s surface. So, assuming that you’re not floating around somewhere in space, you now know exactly where you are. However, GPS receivers normally use at least 4 satellites to improve accuracy.