How the hell do you have time to explain Bitcoin to technically illiterate people? It takes about an hour just to get to the point that the person replies, "I have no idea what you're talking about". The simplest method I could come up with was saying, "It's like internet file sharing except instead of everyone having the same movie file, everyone has the same distributed accounting ledger".
Exactly like I say it: "Like file sharing, but there is only one file everybody is sharing. people with bitcoins has the keys to a little part of that file where he stores his bitcoins. So everybody agrees that you own your coins, but only you can withdraw them."