A simple explanation of a very complex problem? Here goes. Think of a camera tripod. It is very stable because the three legs, no matter what small differences there are between the lengths of the legs, always has the camera at a stable, fixed position. That is the basic principal of satellite positioning. Knowing the "exact" location of three satellites and the "exact" range to those three satellites allows you to calculate your "exact" position. The magic is in how to get close to those "exacts" - and that takes a several years of engineering education in several engineering disciplines (electronics, RF, software, astronautics, meteorology to name a few). One thing to know for now is GPS almost always uses a fourth satellite to get rid of timing errors because in the time it takes for the satellite signals to get to you both you and the satellites have moved.
A second thing to know is there are 6 different GPS type systems in the world. Europe, Russia, China, Japan and India all have their own systems. Getting all these people to agree with each other is quite a chore. And while there is a lot of bad-mouthing of the FAA on this forum the entire world still looks to the FAA for certifying GPS equipment, even if it is not going to purchase it.