Right place, right time, right IP. Casual oriented approach. After that, momentum.
When it came out MMOs were still fighting to break into the mainstream. They were getting close and one of the games of that time was bound to break through. Then Blizzard came out with their own MMO, only it was based on a vastly popular IP. Warcraft 3 was one of the best and most popular games of its time, and if they were to start selling Warcraft brand poop bags at that time, they would have sold. So the mainstream audience was just about ready to try MMOs and then one comes based on an IP they all know and love so it's the obvious choice to give this whole MMO thing a try.
Then the "casual" approach kicked in. WoW was accessible, even in its early days. You could solo most non-dungeon content and you could follow quest chains all the way to the top, which meant no aimless grinding. This is (IMO) what kept people playing - You could quest on your own and get storylines and such, but still utilize social features of MMOs. WoW bridged the gap between single-player games and MMOs.
Now, I'm not an MMO expert. I'm guessing that someone will quote me and tell me that game X did the whole solo questing thing before or whatever. But that's not the point. I AM one of the people who came into MMOs with WoW. I wrote the above from my own experience and the experience of my friends and acquaintances. At that time people were curious about MMOs, but still wary. The Warcraft brand overcame those reservations and once we started playing the game allowed us to play how we wanted. Solo, groups, PvP, etc.
Afterwards, momentum took over. People heard about this WoW thing being fun, so they tried it too. The more people that tried it, the more word got around and the more people tried it. It became the go-to game if you wanted to try the whole MMO thing. It was noob-friendly and all your friends were playing it, so why not? And so on and so forth. I can't overstate the importance of momentum here. As WoW got big, people were exposed to the concept of the MMO, at least by hearing about it and if they decided to check it out the choice of game was kinda obvious. They weren't going to go for some minor title, they want the "big dog".
Finally, it was a pretty good game. This is the "least" noteworthy aspect of the whole thing, but still a factor.
WoW was a perfect storm of conditions (audience getting curious about MMOs), popular IP (Warcraft, duh!), competent developer (this was old Blizzard), correct design decisions (solo and noob friendly basic deisgn), all driven by market momentum. As a result, we're unlikely to see a "New WoW" or a "WoW killer" - it's unlikely that a game will get such a perfect alignment of various factors any time soon. Also, the MMO buble kinda burst and casuals are moving on (mostly to casual gaming, social gaming, smartphone games, etc.). WoW won't die any time soon, it's no longer just a game, it's a cultural phenomenon. But it has started its slow decline.
Over the next half decade WoW will gradually lose their subscriber base. Most of these will not be switching to other MMOs, but rather moving on. They've seen what the MMO thing was about and are ready for something else. WoW will stabilize around 1-3 million eventually and exist comfortably for at least another decade if not more. New MMOs will not reach anything close to the numbers WoW had in its prime and the lucky ones will manage to get 1-2 million at best. More and more will move to some kind of F2P model and the next arms race will be to see who can get the best balance of free/payed content to maximize customer base and profit.
