An insurgency is just a rebellion against the legitimate government. The makeup of the insurgency has been a hot topic of discussion for a while now, and the real answer is that nobody knows its actual makeup. Some groups studying it claim that its mostly foreign. Some say it is mostly domestic. And yet others say its 50-50 domestic and foreign. Nobody really has the intelligence on the ground to figure out for sure.
Heck, nobody even knows for sure if al-Zarqawi [sic] is a real guy, or is even in Iraq.
Its not really like Desert Storm though, no matter how you look at it. In Desert Storm, we knew more or less who we were fighting. Once we forced the Iraqi army to surrender, Kuwait would be freed. Here, we have no obvious objective that will free the Iraqi government to act as a sovereign authority.