Adding backing to your reel before loading the fly line serves several purposes. The obvious reason to add backing is so that if you hook that big one you’ve been hoping to catch and it takes out a lot of line, the leader won’t break when you hit the end of the 90 feet of fly line.
Usually the backing will be 100 or 250 yards of 20 or 30 pound braided Dacron. Since the backing is wound tightly on the smaller portion of the reel the backing needs to be something that won’t retain memory. The backing will most likely stay wound on the reel for several years without ever being straightened. If you used monofilament you would find that as the line came off the reel, after being tightly wound so long, that it would come off in tight coils and most likely tangle if not careful.
You don’t want this to happen when you're fighting a fish big enough to take you into your backing. The backing also needs to not retain water, otherwise mold would grow. The backing also serves to take up space on the center portion of the reel so that the actual fly line is not coiled so tightly. The fly line being wound on the outside portion of the reel allows more line to be reeled in on each turn.
The Arbor Knot is a simple knot for attaching the backing to the reel. It is formed by bringing the backing around the the arbor, tying an overhand knot around the line leading to the arbor, then tying another overhand knot at the very end of the line.