For a long time Pandaria was hidden from the rest of the world. Then, as was inevitable, the land was discovered by both the Horde and the Alliance. Naturally they brought their war with them and now the battle continues in the new lands.
Elder Pandaren martial arts masters, for reasons known only to them, decided that some of the newcomers might be worthy to learn new skills. Perhaps in the hopes of taming their people's battle lust.
Not so wise, after all.
Monkish Resources and Stuff
Like several other classes the Monk uses resources to drive his abilities. How effectively you juggle these will determine how effective you'll be.
Chi - If you've played a Paladin then you'll know how Chi works. You will use various abilities, such as your Jab, to build up Chi points and then expend those points to power different abilities. Fists of Fury, for example, requires 3 Chi to use. Your Chi does not go away when you switch targets, but it will disappear in a few seconds.
Energy - Any ability that generates Chi also uses Energy. Your Expel Harm ability generates one or two Chi (depending on your stance) and costs 40 energy to use. Energy recovers automatically, until it's used again.
Mana - As a Mistweaver Monk you will use Mana instead of energy, but the idea is the same. Burn mana to power abilities that build Chi, then use the Chi powered abilities.
Stances - Monks have three stances, like Death Knights and Warriors, and each of these improves some aspect of the Monk. Unlike DKs and Warriors, you will want to stick to your specific stance at all times.
Statues
These are a bit like the Shaman's totems. Drop 'em and let 'em work. One difference is that Windwalkers don't get to use one. If you're not a Windwalker then you should have your statue down at all times.
Monk Specializations (spec)
Whether you like to beat up on the opposition or heal your allies the Monk has something for you.
Windwalker - This is the "damage" specialization (spec) of the Monk class. Using kicks, punches, weapon strikes, and strong brews the Windwalkers can lay down solid damage over a long period of time, which is great for raids. Their area effect abilities and personal heals will keep them standing even when fighting multiple opponents.
Brewmasters - This is the "tank" spec for Monks. They keep the attentions of groups of enemies while the rest of the team burns those enemies down. While they do much less overall damage than Windwalkers they do a much better job at keeping groups of enemies under control and away from the rest of the team. Brewmasters are also much tougher than Windwalkers and have the ability to shrug off a lot of damage.
Mistweaver - Unlike other healers you will get a direct benefit from doing damage as it will help to build your Chi and your damage also heals nearby allies, so you will be able to do a certain amount of healing just by adding your damage to the team's. For greater healing you use your Chi, as necessary. You can heal at range or stay close to the melee (sometimes not a great idea.)
Now what?
Leveling a Monk is about as easy as any other class. Windwalkers have all the tools and very little down-time, so can go from quest to quest quickly and easily. Brewmasters are slower, but do nicely when they can round up groups of enemies and burn them down. Mistweavers are better off healing a group, though they can plod along at an Ok pace.
Monks are quite effective in PvE content, that is: dungeons and raids. They're fine tanks, their damage is very competitive, and they're fine healers. Not all at once, of course.
In PvP the Mistweaver might be the class of choice. Like all healers they're very hard to kill, so stick with a group, keep them healthy, and they'll destroy everything for you. Brewmasters don't have the damage and Windwalkers lack opponent control and burst.
Still, if you like throwing spinning kicks at player enemies and like a real challenge, don't let ME stop you.