The origin of the phrase 'unmoved mover,' is in Aristotle's Theory of Causality. Summarily, Aristotle postulated that every event (C) logically implies a prior event (B) that acted as a cause for event (C). Obviously then, this implies another event (A) prior to event (B), and so on ad infinitum.
However, logical as the premise of this argument seems, the conclusion (that every event is dependent on another, causal event) seems as surely illogical. In order to avoid an infinite regress, Aristotle theorized that there must be a great "first cause" that is subordinate to no prior event; the cause for eveything without cause, or, the unmoved mover.
As Cletus_the_Foetus exemplifies, there are many that believe this 'solution' to be nothing of the sort. After all, it attempts to resolve one logical inconsistency by providing for what is effectively a refuation of Aristotle's own premise, i.e. if there can be one uncaused cause, then there is no reason why there can't be many.
This appears to sink one argument for the existence of God. Unfortunately, it does more harm to the Big Bang Theory. Whereas a good Christian can always fall back on the ol' omnipotence argument to explain away God's existence as a freak exception to causality*, it makes out the Big Bang to be nothing more than just one more time something blew up.
*So why bother rationalizing at all? I've never understood why these people have to prove everything.