I've re-written the entire metaphor to be a bit more ready-to-use/publish. I would love it if somebody would come forward and help with some graphics. I will be writing more like this one; we can consider this just specifically an analogy to help folks pick the best wallet for their purposes.
If somebody takes the initiative to sketch up some graphics, perhaps following the ideas I've put in brackets below, or just using your own creativity, I will begin a blog and try to write a new analogy depicting a different aspect of bitcoin every week or two. This analogy really only gets across one side of bitcoin, and really only provides info about how to do certain things. I have many other ideas.
This analogy is to help you understand how to keep your coins safe and how to choose a wallet.
Imagine there are a bunch of safes, each with a number printed on them, lined up in a public place. The safes are very secure, bolted to the ground, and no known technology can cut them open.
[graphic depicting a bunch of safes with numbers stamped on them, lined up, in a cloud, hinting at the idea that this public space is actually “on the web” or “in the cloud” in some sense]
Each safe has a slot in the top, allowing money to be dropped in. To get the money out, you need the key that opens the safe. The keys are also very secure, and nobody can pick the lock or open it without a perfect copy of the key.
[graphic depicting a closeup of one of the safes number 253, with a slot in the top and a coin being dropped in it, little cartoon style lines to show that the coin is in motion being dropped in the slot]
Each safe is made of bulletproof glass, so anybody can see how much money is in each safe; but the safes don't have names on them, only numbers, so unless somebody tells you “safe number 253 is mine!” or you see him opening that safe, you don't know which safe belongs to which person.
[graphic depicting safe number 253, with transparent walls, now with a small stack of coins inside of it]
If you want to send Bob some money, you just ask him which safe is his, and he'll tell you, “mine is safe number 253” and you can go drop some money in the slot on the top. Now, maybe Bob doesn't want you (or anybody else) to know how much money he has. But the safe is see-through, made of bulletproof glass, so when you go to drop money in, you can see what he's got, right?
The trick is, anybody can have as many safes as they want. So Bob gets another safe, number 481. When he wants people to send him money, he says “put it in safe number 253,” but then periodically, he goes and takes his money out of safe number 253 and drops it in the slot in the top of safe number 481. Since anybody can drop money into any of the safes, even if you see him dropping money into safe number 481, you don't know that he owns that safe—you would only know he owns it if you see him opening the safe to take money out. So if he ever needs to get some money out of safe number 481, he might expose his secret, and everybody could see how much money he has! But Bob is smart; when he needs to get money out of his secret safe, he always wears a mask, and so nobody can ever tell he owns safe number 481.
[graphic depicting a character in a guy fawkes mask dropping money in safe number 481, which has lots of coins in it]
So nobody can tell how many safes Bob owns, or how much money he has; but if he wants somebody to send him money, he can tell them the number of one of his safes.
Now, for Bob's frequent-use safe, number 253, he has to access it pretty often. When he wants to buy something, that's where he grabs the money from; and when somebody sends him a big chunk of money, he needs to open the safe to pull that money out and stick it in one of his secret safes. Bob is afraid that somebody might steal his key. Somebody could look and see that his safe has a big stack of bills in it, and if they know it's his safe, they might go sneak in his house and search for his key. Bob thinks about hiding the key in a super-secure place; maybe burying it in the woods behind his house where nobody will ever find it. But he has to use it so often! He can't dig it up and bury it again every time.
[graphic picturing Bob with worried expression on face, with thought bubble of digging beneath a tree to bury a coin]
Then Bob hears about Mr. Web Wallet. Mr. Web Wallet and his buddy Mr. Online Exchange offer some services. Mr. Online Exchange (or Mr. OE for short) offers some other services as well, but both Mr. Web Wallet (Mr. WW for short) and Mr. OE offer a key-holding service. Mr. WW or Mr. OE will take your key, and let you choose a username and password. Whenever you want to take some money from your safe, you just tell them your username and password, and they'll go open the safe for you and hand you the money, or just drop it into whichever other safe you tell them to.
[graphic picturing two fat fellows like the banker from the Monopoly game, one with “Mr. WW” on his hat and one with “Mr. OE” on his hat, each looking a bit like a slimy car salesman, that cocky “we're gonna getcha” grin on their faces, perhaps each one with a big key-ring full of keys and another with a clipboard on which there are many usernames and passwords and at the bottom there is a blank line with an X next to it, waiting for Bob to sign up. Perhaps Bob can be pictured in this graphic as well, looking a little skeptical or hesitant, maybe scratching his head]
For a minute, Bob thinks this is great; he doesn't have to worry about somebody stealing his key, because he knows Mr. OE and Mr. WW have good security guards; they have lots and lots of keys from all their customers, and they charge various small fees for their services, so they can afford to spend a lot of money on security. But Bob is still worried. What if somebody robs Mr. OE or Mr. WW and gets all the keys? Or worse yet, what if Mr. OE or Mr. WW decides that they'd rather steal all the money out of all the safes they have keys for and just take off, instead of trying to earn money from their small fees? Bob has also heard that the Government doesn't like Mr. OE and Mr. WW and might tell them not to open safes for anybody without asking them for ID first. Bob doesn't like that, he doesn't want to have to give ID to get to his money and he doesn't want to be vulnerable to theft or fraud.
Bob is about to despair. Suddenly, he hears about Mr. Hybrid Wallet (or Mr. HW). Mr. HW offers a similar service, but with a much better system. Mr. HW asks you to choose a username and password. Mr. HW takes your key and makes a copy of it. He gives you one of the copies, then he takes his, and writes your password on it. Then he chops it into a bunch of pieces so that there is only one letter on each piece. He holds onto the chopped up pieces of your key, and puts them in a little box marked with your username. When you want to get money out of your safe, you go to Mr. HW and tell him your username and password. He goes to your little box of key pieces, and puts all the pieces back together, using your password to guide him. Then he opens your safe for you, and either gives you the money or drops it into whichever safe you ask him to. When he's done, he takes the key back apart into all the pieces, and puts it back in the little box with your username.
[graphic showing a key with a long password (12 characters or more) written on it, then showing that same key chopped into one piece for each character, then showing those pieces dumped into a box with “BobSmith239” written on it and perhaps even that box put onto a shelf full of other boxes with usernames on them]
So Bob goes with Mr. HW, the Hybrid Wallet. He takes his copy of the key, and he buries it under his favorite sycamore tree in the woods behind his house where nobody can ever find it. He rests easy at night, knowing that nobody can steal his key. He knows that if anybody breaks into Mr. HW's secure facility, and steals all the keys, they won't be able to open his safe, since his key is cut into little tiny pieces. Mr. HW doesn't keep Bob's password written down anywhere, and without the password, nobody can figure out how the key goes back together. Bob is no fool; he didn't pick “CAT” for a password, since he knows that would make it too easy for a thief to put the three pieces of his key back together; by choosing a password that's at least 12 characters long he knows that it will be mathematically unfeasible for the thief to figure out which way the 12 pieces go.
[graphic showing Bob sleeping soundly, with a thought bubble showing his key buried under a tree and his coins stacked in his safe and a puzzled thief trying to put together the chopped-up pieces of his other key]
If Mr. HW ever loses the pieces of the key, or gets shut down by the Government, or gets robbed by a thief, Bob can just go out back and dig his key up from under the sycamore tree, go open his safe, and take out his money. Bob is safe and secure.
Choose for yourself based upon your circumstances how you want to store your coins; but remember, if you hold the key yourself, you are responsible for making sure it can't be lost or stolen, and if you let an online exchange or web wallet hold your key for you, you are trusting them to keep your key safe and secure and to grant you access to your safe whenever you want. The hybrid wallet has the best of both worlds and limits the risk on both ends.
If you use a software wallet such as Bitcoin-QT or Electrum or any other wallet which you download and run as a program on your computer, you are holding your own key and must keep it secure yourself. If you use Mt. Gox or any other exchange site, or any "web-wallet," you are letting Mr. WW or Mr. OE hold your key for you. If you use Blockchain.info's Hybrid Wallet, or any other Hybrid Wallet, you are using Mr. HW.
[graphic showing Bob with his key visible in his pocket, an "=" symbol, and then the Bitcoin-QT logo and the Electrum logo; then showing Mr. WW and Mr. OE, an "=" symbol, and then the Mt. Gox logo and the Instawallet logo; then showing Mr. HW (who should look very trustworthy), an "=" symbol, and then the blockchain.info logo]