What do you do?
The first question a total newbie will ask is what do you actually do in the game? What's the point?
Without breaking into philosophy, the point of WoW is that you play a character living in Azeroth. You choose a character class, select a fantasy race, and then go on adventures throughout the world. When you kill monsters and accomplish tasks, you collect experience points; when you accrue enough experience points, you achieve levels.
Despite popular misconception, you don't actually spend a lot of time walking around in character, talking in "thees" and "thous." That's the province of roleplay; while that is a popular playstyle, most people don't pursue roleplay actively. In general, folks just enjoy watching their characters go up through the levels.
What's up with the gear?
As you progress in WoW, you'll hear a lot about gear. These are magic items that you gain through achieve goals and loot from monsters. If your character can use the gear, then you can wear it to gain significant bonuses.
The levels and tiers of gear can get a little complicated. Essentially, bad guys have levels, too. You get better and more powerful gear from high-level bad guys. Eventually, you'll get the chance to earn epic gear; this is the best gear available in the game, although not even all epic gear is created equal. Some epic gear is better than other epic gear; generally, the most recently added gear is the best.
Are there teams?
There are two factions in the game; you can think of these as teams in the broadest sense of the world. The Alliance and the Horde are the two opposed factions in the game, locked in an inevitable, ongoing struggle against one another.
When players engage in battleground, head-to-head conflict, and other forms of in-game war, it tends to be Horde vs. Alliance. The Horde are (generally) Orcs, minotaurs, Trolls, and similar fantasy races, while the Alliance are more common Dwarves, Elves, and Humans. You can't chalk up the history of the factions to classic fantasy, though; any Horde player will be more than happy to tell you how the Horde are noble savages and secretly in the right and so on.
Ultimately, the Horde and Alliance have radically difference feels. They even have different gear, different quests, and much different home bases. In a sense, the Horde and Alliance play separate versions of the game.
Players often have emotional loyalty to their respective factions. Horde players, especially, love to shout "For the Horde!" The Alliance might do the same, but they don't have a slogan with the same powerful ring as the Horde. People really get into their faction choices, though, so much so that some consider making fun of the chosen faction as a taboo.
So what do you actually do?
When you're actually playing the game, most of the action comes down to wandering around and killing enemies. You have a series of abilities that you use against your enemies, and you must move your character out of dangerous areas and effects -- thus, we get sayings like "Don't stand in fire."
You hunt down objects in the world, you kill enemy creatures, and you explore the massive world of Azeroth. While this is a simple explanation, I assure you that the game is huge. The designers of WoW have created what is essentially a massive work of art. And that, essentially, is what keeps us playing this exciting World of Warcraft.
Visit the WoW Rookie Guide for links to everything you need to get started as a new player, from how to control your character and camera angles when you're just starting out, to learning how to tank, getting up to speed for heroics and even how to win Tol Barad.