I like this analogy:
Imagine a massive wall of lockers. Each locker is 1mm by 1mm, and the entire wall of lockers is a square 2 light years on each side. When you choose a private key, you pick one of these lockers at random. When someone sends you bitcoins, there's some magical inbox which puts the bitcoins into your locker without telling the sender anything about the location of your locker.
The lockers don't have locks. If someone knew the location of your locker (ie. your private key), then they could just go take what's in it. Similarly, it's possible to choose a locker at random and find that someone has used it already at some point in the past. But there are just so many lockers that in reality it's never going to happen, even if humanity devotes all of its efforts to searching through all of the lockers.
But it is misleading, don't you think?
It is creating the false image that you are "receiving" coins in your key where in fact nothing is being delivered to you, but instead is stored on another place (the blockchain) and has a little link inside of it saying it belongs to your key.
I think a better analogy would be to call it a wall of
keys like in a parking lot and the
parking lot.
There is the same wall but it contains keys on it. then there is the parking lot (the blockchain) that contains cars (the transaction outputs). When someone sends you a car ("bitcoin"), they don't send it to "the wall" instead they send it to the "parking lot" and only change the key that opens the door of that car.
If someone knows where the key for a particular car in the parking lot is, they can go to that wall, take the key, open the car door and drive away.