It was explained to me as taking a snapshot of the instant the desired behavior takes place, because think about it -- rewarding with praise or treats happens seconds AFTER the desired behavior took place, which could prolong the training. With the clicker they learn to stop expecting a treat but instead expect the clicker to click, because they know if they can get the clicker to click they'll be rewarded.

You also have to "charge the clicker", otherwise it doesn't work as well. To do this you just walk around and click and give a treat after you click, so the dog starts to associate the clicks with treats, like Pavlov's Dog.