Ordinary circles of position in standard celestial navigation are really cones of position. Everywhere on the cone, the observed star will have the same angular distance from the zenith or from the center of the Earth. Some pictures...

Now turn it around. Observing lunar distances, at a known moment of GMT, places an observer on a cone position with its apex at the center of the Moon, instead of the center of the Earth. Those cones intersect the Earth's surface where they are locally lines of position. And where they cross is where you are. Since the Moon is 60 times farther away than the Earth's center, an error of 0.1 minutes of arc in the measured angles yields an error of 6 nautical miles (and worse when the side of the cone intersects the Earth's surface at a low angle). Some more pictures...

The view from above. The cones of position radiate out from the Moon's center. In this case, their line of intersection intersects the Earth's surface in the North Atlantic.

And here's a view looking back at the Earth from behind the Moon. Notice that the cones of position may intersect the Earth in nearly straight arcs.

A view from the back side of the Earth. The cones of position continue through the Earth and intersect on the far side in principle, but of course, in practice, the Moon is not visible from here.