The mono backing stops the braid slipping on the spool (and allows you to save some $$$ without having to fill the entire reel with braid) then fill with your braid then the leader/trace (mostly you will only have a single leader/trace not both).
Sometimes you may wish to have a set up where it goes backing, braid, lighter leader, swivel and then heavy leader (trace) the reason for this is so you can bust off the leader if snagged without losing expensive braid (ie if your fishing 80lb braid it is almost impossible to snap so you end up cutting it off if your in 50m of water thats a bit of dosh compared to losing the leader).
Sometimes a long leader is used to cushion the setting of the hook and allow the fish not to feel the line as braid has no stretch. Sometimes a short leader is used so you have instant feel of whats happening and the hook sets as soon as the rod loads up.
Just to confuse it in some circumstances the braid is the backing and a 100-150m of mono (or more) is attached as the mainline, this usually occurs in LBG situations where extra line capacity is a plus but the abrasion resistance on the mainline and leader is paramount (and to be eligible for records???).
As Kelvin says every situation and target species will be different as will the equipment you are using.
The above is only my interpretation and the way people I learned off fish, there are no hard and fast rules just what works best for you. I just read an article on catching trophy Dolphin Fish and each of the skippers (5 top game charter captains from around the world) had different techniques some stuff was similar but each had his own particular set up.
Cheers, hope I haven't crapped on too long and not muddied the topic up more.
Evil