A:
Fly line backing is a braided line that is directly attached to your spool before you fly line. It is used to not only take up space on your spool, but to provide additional line when a big fish makes a good run.
A typical fly line is only around one hundred feet. If you have thirty to fifty of those feet in the water when a fish hits, you only have another fifty or so to give until he bottoms out and breaks it off.
The backing adds more line for the fish to run out. A typical fly shop will put on about 125-175 yards of backing. Coupled with your fly line, you should have somewhere between 300-500 feet of total line.