Fuel circles are, as explained above, a circle with two fuel figures written in them.
Nothing to do with range rings on a chart!
When the sortie is being planned, the circles are left blank until just before the flight when the expected wind is applied to the flight plan. The figures are calculated and the circles filled in, working backwards, from the intended destination.
The top figure is the expected figure remaining, depending on how much was in the tanks at start up. The lower figure is the figure needed for the completion of the sortie as planned. The difference is (or was in my time) known by the RAF as "combat fuel".
The RAF taught it this way because when en route to a destination it often won't be refuelling (e.g. it will be carrying out a task such as dropping a bomb, or disembarking troops and then return to base or carry on to another destination). An easily assessed "running fuel plan" needs to be kept because if the aircraft was "bounced" i.e. attacked by an enemy, after the pilot had regained his composure, he would know if he could continue on his mission as planned, or not. In combat you can forget all ideas of economical cruise - it's throttles fully forward and mixture fully rich, not necessarily in that order. So, as soon as the position by the next fuel circle is regained, a rapid go/no-go decision could be made.
In the worst case the two figures would be the same, i.e. no "combat reserve" before start up. Having done much of my military service in a helicopter with a shabby 1 hour 25 minute endurance, fuel planning was always a major consideration.