This is a labelled toy model, not a real GPS solver. The map is a flat pretend park, the signal crawls at a pretend 20 map-kilometres a second so you can watch it (real radio moves at about 300,000 kilometres a second), and every ring, meeting point and clock fix is worked out by one small distance model from the same seeded puzzle.
What is real: signals take time to travel; time times speed gives a distance; one distance leaves a ring of possible places; several rings leave one spot; and a wrong receiver clock shifts every range together, so you need one extra clue to fix the clock too. Real GPS does this in three dimensions with four or more satellites, solving for position and clock offset together.
Left out on purpose: the third dimension (rings here stand for shells), satellite orbits and clock corrections from the navigation message, and relativity. No location services are used; nothing about where you really are leaves this page.
Sources: R. B. Langley, "The Mathematics of GPS" (GPS World, 1991), and NASA Space Place's GPS pages. Links are in the project readme.