There are a few reasons for using a leader of mono or fluorocarbon tied to your braid -
Its much easier to tie knots to your terminal tackle with mono or FC.
Braid is opaque and can be easily seen by the fish. A length of leader ensures it is less visible than the braid main line. It can depend on your target - some are very leader-shy (eg. bream) while some are much less so (eg. bass). I know some bass fishos who just tie their lure on to the braid without a leader of any type, but they are in the minority. Probably can work well if they're using one lure on an outfit all day, without changing lures.
Braid is extremely strong and way ahead on breaking strain to diameter ratio, BUT can break from contact with abrasive surfaces (rocks, barnacles...). Mono or fc is more abrasion-resistant.
Braid is very buoyant as you'll notice with new braid. Having a leader of fc helps your lure, especially if using very light jigheads, to go under. On the other hand, if using surface lures, many people recommend using mono & not FC as FC sinks and can impede the action of your surface lure. My tip: you can get around this and use either mono or FC if you're using one outfit exclusively for surface lures by using a very short length of leader (2ft or less).
As for the FG knot - yes, it is a very popular leader knot and has been for at least the last 3 or 4yrs. I tried it and I remember casting the whole leader & lure off almost first cast!! Obviously it is not the knot's fault but my own ineptness in tying the FG knot! Obviously I didn't do it right and for those people who can tie it properly, they swear by it. There are many other leader knots that can be used.
Easiest to tie is the double Uni knot. I can almost do it blindfolded and is the one I use if I have to retie a leader on the water (usually kayak) without glasses on. Big downside to this knot is that the tag end of the mono faces outwards (in the direction of your cast) and with repeated lurecasting can catch and wear until it breaks. The best leader knots, like the FG or Slim Beauty, have the tag end of the braid facing "out". Being much softer, it doesn't catch & wear out easily.
Everything above relates to lure fishing. If bait fishing with sinkers, swivels, etc, you can tie your braid to the swivel and the mono to it as well. Big tip - if tying braid to terminal tackle like a hook or swivel like I do when blackfishing (yes, I use braid as my main line for blackfishing!), you have to double the number of wraps in knots like the half blood knot. This also applies to the double Uni knot for joining leader to braid - the standard number of loops (usually 4) for the mono part and 8 loops for the braid part.
Hope this helps.