What does it mean that McCain pledged to only use "public money" for his campaign?

Exactly where is this “public money” coming from? Is it from my taxes? Does it have anything to do with that checkbox for donating $1 on the 1040 IRS forms? Do people who contribute to this “public money” know they’re contributing, or which candidate will be using their money?

(And yes, I understand that Obama supposedly said he would use public money, but then backed out, and so is using money donated to him specifically. I really don’t want this to turn into a McCain vs Obama question. I’m asking specifically about what “public money” means. Thanks.)