At some point in history, some wood has been buried under your lawn or a tree had fallen / cut down leaving its roots under your lawn. After time the dead wood will start to decompose, and this releases Nitrogen. The Nitrogen release explodes outwards in slow motion, working its way through your soil. The circle of Nitrogen gets larger and larger, year on year.
The large build up of Nitrogen is visible in your lawn, commonly seen as dark green circles of lush grass in the lawn usually after they are a half a metre or so across, though they are visible at first as a tuft of dark green grass.
The Fairy rings may also be first noticed as a group of toadstools manifest in mid-summer. (Sometimes without the dark green grass!) Not all toadstools in the lawn are as a result of Fairy Rings.
Fairy rings start growing from a central point, then gradually radiate outwards in circular shapes. There may be several fairy rings in the lawn at the same time sometimes overlapping - ending up not unlike the interconnected Olympic flag symbol!
Generally, the grass inside the circle is lighter green - if not brown, whilst the grass just outside the circumference of the circle is slightly darker. This a result of Nitrogen being released - or activated.