A ring main wiring circuit is the alternative to a radial wiring circuit. In a radial wiring circuit, the wiring starts at the circuit breaker and connects to each device on the circuit (fans, outlets, lamps, etc) in turn. When it reaches the last device, the wiring simply ends.
Ring main wiring goes one step further: instead of ending the wiring at the last device, it pulls more wiring back from the last device to the circuit breaker, completing a loop. Ring main wiring is required in some places, and illegal in others. Modern homes in the United Kingdom tend to have a ring main setup.
The main advantage to a ring main system is smaller wiring. Since each device on the ring has two hot wires connecting it to the circuit breaker (one on each side of the loop), smaller wiring can be used to safely carry the electric current. Smaller wire is both cheaper and easier to work with -- it bends more easily, can be pulled around corners with less effort, and is easier to fit into the screws and connectors you need to attach it to.
One other advantage is wiring distance. Wire has some small amount of resistance, and the longer the wire goes to reach the device it is powering, the more resistance it has. This results in a voltage drop over the length of the wire run (by Ohm's Law), which could affect the operation of your electrical devices if it drops too low. The maximum distance from the circuit breaker around the ring is the midpoint of the ring, while the maximum distance in a radial circuit is the end of the chain. In this manner, the ring setup effectively cuts the distance to the farthest device in half.
The radial system does have one advantage over ring main. If a break were to occur somewhere in the wiring loop of a ring main system, you wouldn't know it. Everything would still function normally because it is still powered from one end. However, this means that if you took advantage of the ability to run smaller wiring (and everyone does), your wire is now undersized for the current it is expected to handle because the system is no longer powered from two wires, only one. This can result in overheating of the wires, which in turn breaks down the insulation and can start a fire.