Lieutenant General Odierno explains the surge in this speech.
The key was to hit Shia thugs as well as Sunni Arab terrorists to eliminate motivation to join militias or ally with al Qaeda to defend their own neighborhoods. The problem was that these groups took an "expansive" view of defense and just provoked the other side.
Also, we needed to hold what our troops cleared because Iraqis not strong enough. The surge weakened the enemy and gave the Iraqis time to get good enough to hold against the weaker enemy's efforts to regroup. How good will determine how quickly we draw down.
And a December capture of al Qaeda documents was key to making the surge work. I was worried about a pointless surge early last year, and if not for this capture, that's what we might have gotten. The documents highlighted the importance of the Baghdad belts and gave us an objective that hurt the enemy.
And while the surge exploited some existing trendlines, the surge was not irrelevant to pushing those trends forward. For me, this is amazing logic. The anti-war side said the surge was doomed (and some still do) yet now many of them say the success we see now had nothing to do with the surge. It's like arguing that D-Day had nothing to do with winning World War II because the trends prior to June 6, 1944 were already in our favor.
Let's keep our eye on the ball. While they are reduced in power, the enemy is still out there.