The linked article does neatly, but they use 2D projection (so it's circles not spheres). Very simplified you use the broadcasted position + timestamp of multiple GPS satellites to find your location on the earth. So for a single satellite, you can (using time-in-flight of the signal) estimate the distance to that satellite at a point in time when you received its data. Once you know the distance D to that single satellite, you will know that your position (within margin of error) is anywhere on a sphere with the satellite as its center and radius D (of course this is a bit silly as you know you are definitely not farther away from earth surface as the satellite but rather somewhere 6000-6500km away from Earth center). So when using multiple satellites, you get a set of spheres and (simply viewed) would intersect those spheres - you will be somewhere in this intersection. Now if you can safely assume that your are always on the surface of the earth, you would project this (3d volume) intersection to 2d onto the earth surface - this projection is rather "small" hence less error. But if you would project this intersection using any other 2dimensions, the resulting area would be "wider" in terms of height/depth relative to the surface.

You have to picture those spheres given that the satellites are roughly at same orbital height relative to earth center and you always receive signals within your "field of view" on the nightsky - and of course assume the earth is round.