This whole war on terror thing seems rather all over the place doesn't it at times? What does Iraq have to do with 9/11? Americans asked the same questions in 1942 when Americans were attacking French soldiers in North Africa -- what did France have to do with Pearl Harbor?
Wars only seem neat and tidy in hindsight. Only when all the facts and information are publicly available after the events are over can the tangled web of a global strategy be made to make sense.
This war is no exception and because of the complexities of international relations in this day and age, the strategy is even more convoluted. So here is my succinct way of explaining what the US strategy is based on the past 2 and a half years of following these details on a daily basis.
On 9/11 thousands of Americans were murdered by Islamic extremists who crashed planes into buildings and such. This was really the culmination of nearly a decade long series of attacks by the same group of extremists calling themselves Al Qaeda.
As a response, the USA declared war on all international terrorist organizations and the states that support them. Iraq, Iran, and North Korea were explicitly put on notice in early 2002 as the "Axis of Evil" as states that support terrorism. Contrary to some claims, Iraq was never linked to be part of the 9/11 attack, they were simply one of the leading overt funders of international terrorism.
The first battle was in Afghanistan which was to remove the Taliban regime which actively supported and aided the specific group responsible for 9/11. Once the Taliban regime was removed, the US moved to stage 2 which can be described as "draining the swamp" phase. That is, trying to change the environment in that part of the world that creates terrorists.
Part of that stage 2 plan was to remove Saddam Hussein in Iraq. Iraq had been funding terrorism and it was believed (correctly as the Kay report makes clear) that Saddam had WMD programs that, eventually, would have yielded serious weapons of mass destruction (WMDs) which could then be delivered to terrorist organizations who would be more than happy to deliver them to the United States. It was also believed (wrongly as the Kay report makes clear) that Iraq had vast stockpiles of chemical and biological weapons that could in the short term be used against the US. These stockpiles were, unfortunately, used by political leaders to create a sense of "imminent threat". This was particularly the case in Britain where Tony Blair explicitly made the case that Saddam was an imminent threat (in the US, Iraq was not pushed as an imminent threat as much as simply a threat that the US could no longer tolerate in a post-9/11 world).
So the US and its allies (UK, Australia, etc.) went into Iraq with the primary objective to remove Saddam and as a secondary objective to "drain the swamp" by putting into place a stable government that would, ideally, be a representative democracy (the same thing they're trying to do in Afghanistan).
If you look at a map of the region, there are 5 major sources of terrorists (or were): Going east to west you had Afghanistan. Then Iran. Then Iraq. Then Saudi Arabia. And finally Syria. If these 5 states can be converted to stable representative democracies, it is believed that the terrorist problem will largely dry up (or at least be degraded to a manageable point).
Diplomatically, the United States can't just go east to west overthrowing regimes. It has to have a casus belli (justification to satisfy international sensibilities). 9/11 gave it a casus belli for Afghanistan. The UN resolutions against Iraq and violation of the 1991 cease fire gave the US a casus belli in Iraq (barely). But there isn't one for Syria, Iran, and Saudi Arabia. That brings us to phase 3:
The Bush administration's goal is to make Afghanistan and Iraq stable prosperious open societies that will increase the rate of westernization of Iran, Saudi Arabia, and Syria in the hopes that those countries will open up and become less repressive (or as Dr. Rice put it "End the freedom deficit"). I am skeptical, especially given the idiocy of a handful of US soldiers in their horrific mistreatment of Iraqi POWs, that this is an achieveable goal.
I fear that the US won't be able to do what really needs to be done in the middle east until a major US city is destroyed by a nuclear weapon smuggled in by terrorists from Iran, Syria, or Saudi Arabia. At whic point, gentler responses will no longer be available.
For Americans such as myself, that is really what this is all about. in the 90s it was bombs and such against US personnel overseas. In 2001 it was the spectacular hijacking and crashing into the world's largest buildings murdering thousands. What we don't want to see is in the 2010s nuclear weapons being smuggled in by these same groups. That is the end goal - to stop these groups now or at least try our best.