I looked at that, but unfortunately there's about as much misinformation as worthwhile comments there. And I couldn't find any that match what I've always taken to be the explanation: that there's an energy threshold to be overcome.
Imagine e.g. that the two surfaces are made of materials which, if completely flat, would have no friction at all. But instead of being flat, each consists of parallel ripples. At rest, the two sets of ripples interlock. A small amount of energy needs to be invested in lifting the block over the ripples, but that energy is then available to get it over the next ripple, and so on.
It needn't be physical ripples - it could be some electrostatic bonding, but the concept is the same.
So I did a quick search and found this
http://www.khanacademy.org/science/...on-on-static-and-kinetic-friction-comparisons