The reason behind the war was because, after 9/11, the USA (or its head honchos anyway) felt they had to do the playground equivalent of beating up a much smaller, much less popular boy to make itself feel big again.
The reason that British troops are there is that Tony Blair was so excited at the thought of the US president being his bestest friend, that he would have done anything to keep in with him.
As to what they're still doing there, to their credit, is staying behind to at least try and do something about the complete mess they have made of the place rather than just leave it.
Will try to hunt out the links, but during the main body of the war I used to read the news on some website that had transcribed Russian intelligence reports. If you read them with about a two week time delay, they were surprisingly accurate compared to the official versions of events.