Our strategy center is having fun with this one, but what they say rings pretty true. I borrowed a lot of this from the stuff I've been reading and my involvement in some of the recent conflicts, but here is what I think.
To understand why Russia invaded Georgia, you've got to go back and look at events from the breakup of the USSR until now. Originally, we assured the Russians that we would not seek NATO members among the fractured states that split.
Whoops, we did that. For the right reasons, but we still did it.
While Russia became mired down in Perestroika, their economy faltered and their once proud military might began crumbling due to the lack of income to pay their soldiers and modernize their equipment. This increased their uneasiness since it emphasized a weakness. Meanwhile, we were doing all kinds of exercises with global partners (think COBRA GOLD, IRON COBRA, RED FLAG, etc)
Then, if you look at the Bosnian/Kosovo campaigns, you have Russia disproving the claims made by NATO members of the actual events, resulting in both China and Russia blocking any UN involvement. So, instead of the UN coming to the rescue, it was NATO despite the Kremlin's objection and their allegiance with Serbia. It was only after the conflict was settled that the Russians were allowed to play a minor role in the peacekeeping force. Then the final divisions of land were contrary to what the Russians wanted.
All of this begins to paint the picture of a Russia in decline with decreased influence over world matters.
Then throw in our significant advances in ballistic missile defense, and now we are really taking away the last trump card the Russians had.
Georgia is a significant ally in that sphere and their generous gift of overfly rights to DoD aircraft supporting OEF and OIF from European bases enabled a large amount of our ops. If I remember correctly, Georgia was petitioning for NATO member status. The 2 sections, S. Ossetia and I forget how to spell the other, are both sympathetic to Russian ideals and consider themselves Russian and not Georgian, much the same setup as the Serbian/Kosovo ethnic concerns.
Russia, in an attempt to regain some importance in world affairs needed to get some recognition. After a decade of quiet, Russian Bear bombers and recon aircraft began trolling the western seaboard again much like Cold War days. This was no small blip to the US, as we responded with alert fighters escorting them.
The US, meanwhile, is tied up in operations in Iraq and Afghanistan. With the majority of our forces tied up or in reconstitution, the US would be hard pressed to respond to anything outside the narrow confines of our present conflicts. Russia had the perfect opportunity to deliver a black eye to the US. By asserting themselves to rescue "ethnic Russians", what you see is Russia playing on the Bosnian/Kosovo theme in Georgia. This time, we cannot respond and NATO is tied up with operations in Afghanistan. Wonder why we haven't responded in massive form? There it is.
By taking advantage of this opportunity, Russia was able to post a major coup and show other potential NATO as well as new NATO members that US promises of assistance and protection are largely hollow.
It will be interesting to see how Medvedev spins all of this.