Fly line is what makes fly casting possible. The plastic coating gives it mass — enough to bend the rod tip on the back-cast and unfurl it forward. A leader and tippet (much thinner) attach to the fly-line tip, then the fly.
Densities: floating (the default for trout, dries, and most nymphs under indicators), sinking (for streamers in deep water), intermediate (sinks slowly for in-between fishing). Match the line weight to the rod weight — a 5-weight rod casts 5-weight line.