Fly line backing serves two basic purposes. The first is to fill up your reel so that your fly line completes the filling of your reel to within, say, 1/8th inch of the spool capacity. The second is to still stay connected when a big fish strips of all your fly line!
For most purposes, the No Frills backing is perfectly adequate as a trout backing line. If you require a stronger line, say for salmon fishing,then you should consider another backing line on this counter.
If you are using small reels and have limited space for the backing but require a long length of it for big fish - then, again, you require one of the more advanced backings. If you want to reduce tangling with backing and have a seamless, no-knot connection then choose one of the braided backings.