The fairy ring mushroom grows on lawns, where the fungus decomposes organic matter. It often grows in a configuration called a fairy ring: a spore germinates, and a fungus grows. When it uses up its food supply, decaying organic material in the soil, it dies there. But there's more decomposing material at the periphery of the fungus' position, so it continues to grow there, forming an ever-expanding ring (some of which those with very shallow angles may be hundreds of years old).
When the fungus creates mushrooms, the mushrooms come up in a ring. And because of the uptake of nutrients by the fungus, the grass above the ring barely grows. And when the fungus dies, it fertilizes the soil, and the grass inside the ring is greener and more lush.