Sorry: military doctrinal term.  Very roughly, the center of mass is that which allows one force to influence another.  The center of gravity is that which, when removed, prevents the exercise of power.  The idea behind the modern maneuver doctrine is to identify and destroy your opponents center of gravity, vs. his center of mass.  E.g. Who cares if the Soviets have 20,000 tanks if they can't get fuel for them; 20,000 metal pillboxes aren't nearly so dangerous.

For example, in the former Iraqi regime under Saddam Hussein, the center of mass was the Iraqi military; the center of gravity was the government.  Al-Qaeda's center of mass is probably just its personnel.  Al-Qaeda's center of gravity, on the other hand, is far more difficult to determine.  It's not Al-Qaeda's leadership alone--the West has destroyed much of that, yet the organization remains dangerous.  One might argue that it has multiple centers of gravity, each of which must be destroyed/contained/weakened: madrassas promoting its idealogy; implicit support throughout much of the Islamic world; etc.

In Elemental, one center of gravity is almost certainly the Channeler: if s/he goes down, game over.  Whether or not the Channeler is a center of mass is likely a play-choice: do I have an amped up Channeler who eats armies for breakfast, or do I spread out the Essence into other things?  For some factions, a center of gravity might be the economy, while the center of mass is the Bear Cavalry.

Does this explain the concept well enough?

Roughly, yes, though I would argue that Sauron's center of power was less in himself, and more in his armies and captive nations.  His center of gravity was certain the Ring, however.  Indeed, the conclusion reached by the Council of Elrond was that the West could not defeat Sauron through military might alone; that is, they could not face his center of power directly.

Fun fact of the day: This decision, perhaps more than any other, shows Elrond's willingness to abandon the hopes of the Noldor in Middle-earth; his ancestors had tried continuously to garner victory through military might, and for nought.  Galadriel, it seems, still held out hope for a permanent rulership in Middle-Earth: even after the fall of Beleriand, she founded Hollin, and after its destruction she founded (or, perhaps more accurately, took rulership of) Lothlorien.  Her final decision would come later.

Sorry - I'm a total Tolkien geek. 

I'm glad I'm in good company, at least.

Good trivia. 

Since Galadriel's come up again, I'd like to refer the newer folks to a swell old thread from Ynglaur on Gameplay Types.

That thread left me with an enduring impulse to question the deceptively simple phrase "victory conditions" and wonder if the genre would gain by generally shifting to a new name for 'the same' thing that was more like "closure conditions" or "game over criteria." Mind you, that's all tied up with my being a role-player at heart and a card-carrying member of the "it's not the kind of game that you can win" faction.