GM neutrality is the bedrock on which old school play is founded. The GM is objective arbitrator, referee, judge. He is neither against the players nor for them. He presents them with the world they interact with, and he provides the consequences for their actions.
I elaborated a bit further:
No human being can be totally neutral, but he can try. That's really what it's about.
There will always be some level of illusionism, because in giving the players freedom they'll go where you don't expect, so you have to just make shit up (NPCs, locations, etc.). You try to do this as "neutrally" as possible by thinking to yourself, "Okay, in this game world, what would happen? What would be here?" Not what would be "fun", not what would be a challenge, not what would kill your players, not what would make a good story... but what would happen.
Random generators help a lot to keep you honest. Roll the dice and go with the results, and don't ever fudge.
That's what I think it's all about, really. If I was listing DMing best principles, or drafting a manifesto, there would probably only be three points:
- Try as hard as you can to be neutral.
- Think about what would happen, not what would be fun, what would be a challenge, what would kill your players, or what would make a good story. Just what would happen.
- Use lots of random generators to keep yourself honest.
None of these points are actually realizable 100% of the time. We are human beings, and human beings are flawed. But you can try as hard as you can, and you'll get better at it. (As Zeb Cook put it, you need to "Take the time and effort to become not just a good DM, but a brilliant one." A big element of that is training yourself to be neutral. At least as far as my own DMing preferences go.)
The platonic DM is, basically, a deistic God who is utterly objective and dispassionate. And being a deistic God is not really such a bad thing to aspire to.