If you move horizontally, you're getting closer to one satellite and further away from another -- the changes in GPS signals add, just like if something you're looking at moves from side to side. If you move vertically, you're getting closer to or further away from all the satellites at once; but since GPS relies on the differences between signal arrival times, that's much harder to pick up.

Thanks I think that's the best explanation I've read!

Thanks! It's unfortunate that the diagram on wikipedia is actively misleading since it corresponds to known distances rather than known differences of distances.