I've had to do this so often I've practically got it down to a science. In fact, I did a three part oral presentation on 'What is a Role Playing Game' to pass my communications class.
The basic gist is to start out by getting common ground with the person before getting into the technical aspects of it, so I generally don't start the explanation by trying to explain what a modern RPG is. Instead, I begin something like this:
"Remember when you were a kid you used to play games like 'house' and 'cops and robbers' and 'cowboys and indians' and all sorts of other games were you used your imagination to pretend you were doing something else? In essence you were playing a very simple role playing game, and as a kid you probably enjoyed it alot. Everyone was played role playing games at some point in thier life. Over time, if you kept playing games like that, they got to be more and more complex. You started using more realistic props you invented scenarios and tried to tell stories. Eventually however, for a variaty of reasons, such games lose thier charm. One of the most common frustrations children have playing 'Cops and Robbers' is the problem of consensus. If I pull my gun out and say, "Bang, I shot you.", you have to concede that I've indeed shot you. At some point though, you get tired fo being shot and say, "No, you missed, BANG! I shot you." then I'm forced to concede that indeed I missed or else the game ends. Because, if no side concedes, it quickly deginerates into 'No, you missed!' NO, YOU MISSED!', and so forth. People that continue to play role playing games come up with means of arbitrating those disputes. For instance, you might decide that any time there was a dispute, you'd play rock-paper-scissors to decide who would have to conceed. Or, you might decide to start carring paintball guns and decide the more directly. However, if you decide to play the game with paint ball guns, the outcome is no longer dependent on your imagination. You can't decide to be different than you are, though you could of course pretend to be something other than a weekend warrior in a converted cow pasture. Returning to the rock-paper-scissors game, an intelligent child might decide to give everyone in the game some advantage. For instance, Bobby was a 'Sure Shot' and when he shot you, you had to beat him two out of three times in a rock paper scissors game to make him miss instead of only one. Jane was 'Dodgy', which cancelled Bobby's 'Sure Shot' because to hit her, you had to beat her two out of three times in a game of rock-paper-scissors. Tim was 'Tough' and had to be shot twice, and Sue was the 'Police Chief' and could get you to surrender without a fight if you lost a game of rock-paper-scissors to her. AND that is a role playing game.
Modern RPG's typically use very complex systems to describe each persons advantages and arbitrate disputes. Typically, one person acts as a referee and pretends to be every imaginary thing in the game that isn't one of the persons (or things) that the other players are pretending to be....."
And so on and so forth, with the level of detail modified to the intelligence, educational level, age, and interest of the person asking the question.