The general idea is that the "click" sound becomes a marker to tell the animal he's done the right thing, and a promise of a more tangible reward to come later. As opposed to giving a bit of treat every time the animal's done what you asked, for instance.
Here's a good book about positive reinforcement in general, which also includes clicker training, though it's not an extensive training manual:
Don't Shoot the Dog - by Karen Pryor
http://www.amazon.com/exec/obidos/ASIN/0553380397/qid=1101314015/sr=2-1/ref=pd_ka_b_2_1/102-3939116-5196115As I remember, clicker training was originated by mammal trainers at Sea World, and then applied to other species.
Personally, it's not my thing. I have enough trouble keeping a leash and other paraphenalia in order, that I don't want to be bound to a clicker device that I have to carry around with me at all times. But you can achieve the same thing with just your voice. Use a word in place of a click: "Yes!" or "Good!" spoken enthusiastically, and that becomes a reward in itself. I also don't think there's anything wrong with using food as a reward, but you'll want to wean your pet off of expecting a treat every single time. Once the desired behavior is established, keep the reinforcement schedule intermittent and random - that's been shown to give the best and longest-lasting results.