These tend to grow out of the decaying roots of a tree or large shrub that has been cut down in the past. Oftentimes, the stump has been removed or ground to a level below the lawn surface leaving the radiating roots close to the surface of the ground intact. It can take only a few, or sometime a lot of years before the mushrooms appear. Since the roots grow in a circular direction from the center of the stump, the mushrooms tend to grow in a circle. Hence, the term "fairy ring". Many people in subdivisions are surprised when these appear because they had no idea that the land developer took down the trees on their lot before construction began.
There are other theories as to why some mushrooms tend to grow in rings. For more information, here is a link to a Wiki article:
http://en.wikipedia.org/wiki/Fairy_ring
Good luck with all of your gardening this year.