well there have been several very good explaination of fairy rings.. we had one because we cut down a rotten old apple tree, but didn't dig out the roots.
a ring forms as the roots rot. it starts close to the trunk, and as it expands, it naturally form a ring..getting bigger(the ring) each year, as the mushrooms get smaller.. fruiting bodies would appear every spring, or after a heavy summer rain.

in side a fairy ring, you can incant a verse, and it will make a wart disappear, or make a wish, and its sure to come true, just as a lie is sure be found out. (needless to say this is last one is very useful to a mother, since our fairy ring took up half the yard!)

and yes i do have poor soil. i live on top of hill, half of which has been carted away-- on the edge of old sand mine. even with years of composting, the soil is still mostly sand.