Backing on your fly reel is an essential piece of gear. There are a lot of benefits to having good backing on your fly fishing reel. Fly reel backing is normally made of dacron or braided polyester, it is the first layer of line you will put on your fly reel. Backing is a braided line made up of many small strands. It comes in many different tensile strengths.
You need fly line backing to fill up the extra space on the reel. (For the same reason you would use a large arbor reel) To allow you to take up line faster. With only fly line and no backing on your reel, you will not be able to reel in as fast as you would with backing. You also need it in case you hook a large fish, because the fish needs to be allowed to run. With no fly line backing on your reel, the maximum the fish will be able to run is the length of your fly line.