I'm glad I'm not the only one that keeps using water to explain this! :-) I have the analogy slightly different:
"Imagine a bath full of water. Beneath the plughole is a bucket. Your job is to exactly fill the bucket with water.
You can control three things; the size of the plughole (aperture), the size of the bucket (film speed) and the amount of time that the plug is out of the hole (shutter speed)."
I generally elaborate with Delta 3200 being a thimble, Velvia being a whacking great barrel and so on. Once they've grasped the "double the size of the plughole and then either a) double the size of the bucket or b) half the time the plug is out of the hole" and all the permutations you can explain about film grain, colour saturation, d-o-f and blurring in small easy stages.
The problem with analogies is that it's easy to sound damn patronising when using them, so I usually start off with a warning that this is a noddy-level explanation and a pre-emptive apology!