From an egghead standpoint, they usually form over bodies or overly rich soil in the right spot. The mushrooms are an invasive species that feed over the richest spot in the center. As they deplete the resources they spread out, leaving the middle empty and sometimes with toxins not allowing other plant growth. Hence the circle with the bare patch or only light grasses.
I have gone back several times at midnight, no dancing fairies or goblins so far.

Based on what I learned in biology class, that's not exactly accurate.
Mushrooms grow in rings because they are sprouting from the edges of a huge mother mushroom below. Fungi are the most durable/widespread species on earth. They take rotting animals, dead leaves and plant life, even toxic substances, consume them over time and convert those elements to useful and beneficial food for trees and other plants.
Speaking of huge mother mushrooms, if I remember correctly, forests of Alder trees... Aspen trees... something like that, come from a huge mother fungi below ground.