Welcome to the forum and the world of Play By Post Roleplaying! My name is Professor Oak and...
Erm.
Basically the long and short of it is, the GM is the individual who comes up with the concept of the game, the story, and all the miscellanea that goes into running a game (accepting applications, running the story, keeping things moving when they slow down, et cetera). It's pretty similar to the concept of a DM in Dungeons and Dragons, where one person is basically narrating the plot and coming up with encounters for the rest of the group, only in PbP roleplays, it's a lot more free from and more often than not, GMs like to have their own personal characters in the story to interact with other player characters. It's basically their job to say, "Okay, this is what this game's about, here's the rules and expectations, and here's a character sheet for you to fill in. Okay? Now we're starting the game, here's the setting of where you guys are and what's happening, and as you guys keep moving along, I'll keep introducing stuff for you to interact with so we can keep the story going."
They're pretty much needed whenever there's a dispute between players that requires mediation. In most cases, a GM's word is law, so a good GM has an unbiased opinion on matters between people and goes with what's best for the game/ most fair. They're also the primary drivers of the story, maker and controller of NPCs, and so on so forth. The GM's basically a key for a game running smoothly, although players do need to do their part and participate.
Take a look at some of the RPs that have been around for a while with a healthy number of posts and pay attention to who the GM is and what they're up to. It should give you an idea of what's expected.