The Online part is obvious, the "Massive" part is subject to opinion. And the "Multiplayer" part is subject to interpretation. For example, some would argue that the "leveling" game in a MMO like WoW is not Multiplayer at all. Whereas, I might argue it is Multiplayer by virtue of it being a shared world.
I was reading an entry over at KTR about Cultural Differences and I was struck with a thought. I think, at it's core, the defining characteristic of an MMO is shared experience. Or more specifically, a shared gaming experience with hundreds of strangers.
Now traditionally, this shared experience is in a Persistent Online World (POW), but I don't think a persistent world is really the defining trait. Lots of MMOs have sharded worlds or very little persistence. In fact, I would argue that if you start with UO, the trend has actually been to move AWAY from persistence in MMOs.
But the one commonality in all these games is shared experience.