This relates to why you will often see multiple mushrooms of the same type blooming at the same time in a ring pattern: the edge of the ring is the periphery of the linearly, radially expanding mat of subterranean fungal fiber weave, which produces fruiting bodies at its edges.
The inside of a fairy ring dies off as it uses up nutrients.
The leading edge of the circle remains alive so that is why the fruiting bodies (mushrooms) are there. The fungus produces nitrogen which leads to the growth of a greener ring of grass.
The ring’s steady expansion is driven by growth of the underground mycelium (not spores).