I have wondered this as well... Maybe we should review the shows? I know Tenzin got his butt whooped by Zaheer, so masters are not unhittable. They also do not instakill (at least the "masters" I've seen.) On most bending servers I go on, there is no fine line between good and bad benders, there is always benders who don't know what bending is, or how to use it, then benders who are just starting and usually spam one move, but don't use it well, then benders who can use a variety of moves, but still don't use them well, then benders who use a variety of moves well, but don't know many combos or techniques, then benders who know combos and techniques, then benders who use all of the abilities well, as well as the combos and techniques, but cannot seem to flow them together. And then I believe a master can use all of their abilities, combos, and techniques fluently, like they've been bending their whole life.
The official definition of master is - "a skilled practitioner of a particular art or activity."
But you cannot always identify who is skilled and who is not, because there are multiple tiers of skill, as I demonstrated above. A bending master does not have a certain definition, unless your server has master titles or leaders, then you can call yourself a master. But, I believe a bending master is a bender who can use all of their moves not only well, but fluently. Masters are not invincible, and I've never seen a "master" instakill, unless you're talking about in a matter of a few seconds.
So, there's no real definition of master, at least for bending.