Traditionally, a designated person given responsibility for some or all of the GMing Tasks. Since the actual tasks and authority over them varies widely across role-playing, this term has many different meanings. See GMing Tasks.
A huge problem
Said with a special emphasis in gaming culture, the phrase "the GM" implies that the GMing-tasks are concentrated in the hands of one person. I submit that this is a historical artifact and that Leadership and Authority are not the same things.
Leadership is a sort of elected or consensually-recognized social status, involving looking to a given person's judgment about stuff. The key point about being a leader is that one can't grab and hold leadership; it is only granted, and it's always subject to revision by the led, at the very least through suggestions and even through non-painful transference of the role. That's important.
Authority is a division-of-labor issue. A lot of things need to get done in this particular endeavor, and you do this, and I do that, he does that other thing, and when X comes along, he and I will take care of that as well. This is best understood, I think, as a way for a person to know he or she does not have to do a certain thing, yet can rely upon it being done. One of the implications of looking at it this way is that challenging authority is not really done, not if everyone's doing his or her job, and suggestions are emphatically only suggestions.
At its root, nothing is wrong with centralizing the details of either or both into a single person. But how their parts interrelate in doing so has typically been parsed in a fashion that swiftly leads to problems. Consider the order of this list:
Creative leader: Color and Reward
Procedure leader: Techniques
Primary authority holder, if any – application of a given Technique
If any of these functions are to be centralized in any formal way, then the order I've put them in (top-down) should indicate which supercedes which, looking at any two of them. And that going the other way is rife with potential social/structural flaws.
I suggest that nesting the concepts from bottom-up causes problems for extremely basic social reasons, not specific to role-playing at all. Here's an example.
Let's say Bill is a good procedural leader, but happens not to be the person who holds situational authority in a particular game, who is James. James is thus nominally "the GM," and part of his job (in this game and group) is to set scenes and play NPCs. So, James goes ahead and sets a scene or has an NPC do something, but in a fashion that doesn't fit with what's been done or understood to be done so far. Bill steps in and says, wait a minute, that's not following the procedure, let's back up a minute. Wham. Power-struggle.
Why? Because, I suggest, everyone inherently knows that a thing is only fun insofar as someone doesn't violate the procedure everyone else thought was the way to do it. James' authority over doing it is inherently not the same, and not as powerful, as whoever-has-authority over how to do it.
However, in this case (gaming), everyone shares the same verbal illusion or delusion is that it does ("situational authority over the fiction emcompasses procedural leadership in general"). So James gets mad and everyone gets nervous, because (a) they want James to do his job, but (b) they do trust Bill in his understanding of the procedures of how Bill should do it. So now it's cognitive dissidence - by supporting Bill, they mistakenly think they'll undermine James in his function, but by supporting James, they correctly know that procedures will now be up for grabs, and they don't want that either. The whole concept of "the GM" then blankets this mess and turns it into an indigestible, stinking hummock.
If I'm right about that, then the worst-case scenario would be ...
a) Calling a person "the GM" because he or she holds the bulk of the four types of authority.
b) Then assuming that the same person, because he or she is "GM," automatically is the social/procedural leader; and continuing up, the creative leader (i.e. we smush the three creative subtypes together)
c) OK, now we look up to the social level and where all all three social subtypes are smushed there together too (social organizer, host, rules-owner and suggester).
d) And finally, since this "GM" exists as a total helmsman over the smushed-together creative level, it is now presumed that he or she is also the main person involved in the smushed-together social level.
Gee, that's funny, the worst-case scenario seems to be what a whole lot of people do. So either I'm entirely wrong and all those people are happy as clams, or I'm pointing out some very negative embedded traditions in our hobby that should be reconsidered as soon as possible.