Full of folklore, the reality is that fairy rings are where a circle of fungi enriches the soil causing a marked ring of stronger growth:
This photo, taken on a sunny day, shows an almost complete circle of lusher growth with the fruiting body of the fungi (toadstools) also showing. This particular fairy ring is in one of our chicken runs. There were also a few other, smaller, rings but these were too indistinct to photograph.
This next photo is of the same ring but was taken early in the morning on a duller day:
Here, I have got lower down to show better the fungi growing in the ring. You can also just make out that the grass is longer and thicker in that area.
The full set can be seen in the Garden Gallery.