Garst from Stonemaul has a really interesting question on the forums: where can a lore newbie go first for information?
Recently, I've been trying to get more and more into the lore of Azeroth-- instances especially are much more fun to play when you know exactly who you're fighting and why they're doing what they're doing. In the thread, Neth recommends a few books-- Day of the Dragon, Lord of the Clans, and The Last Guardian, and I agree with her in recommending scanning through (it's long and sometimes boring) the timeline of the WoW universe over on the website. For all of my interest in it, the only thing I've really done outside of the game is go back and replay Warcraft III (or just watch a few cinematics from it). Both Wikipedia and WoW Wiki have lots of good lore info. And one thing Neth doesn't mention is that there's lots of lore inside the game itself. Don't laugh, but especially in Scarlet Monastery and Scholomance, reading through a lot of the books laying around will give a really good background on what's happening in Azeroth.
You're laughing, aren't you? Ok, well, a lot of players may just say "lore lol," but believe me when I say that giving the history a read definitely fills out the game a little bit, and shows you even more deeply the care Blizzard has taken in putting this universe together. Wielding Ashkandi is fun, but it's even moreso when you know who that sword used to belong to.