You would import the private key with a tool like Pywallet, or with your Bitcoin client patched with sipa's key import/export patch.

It's useful mainly for so called "paper wallets", you can save the bitaddress source code to a thumb drive, load it up on a computer never connected to the internet, print the address and private key, and send your Bitcoin savings to that address.

Ten years later, you'd be able to import what would then be either a couple of million-dollar-sport-cars, or just some stupid cryptocurrency not worth the paper the private key is printed on.

Sure, no problem.

I also just remembered MtGox allows importing of private keys in their "Deposit" section. It's a really nice practice if you've got a lot of Bitcoins.

You can experiment with the import of private keys at strongcoin.com as well.

The bitcoin wiki is loading slowly lately, but contains some info:
 - http://en.bitcoin.it/wiki/BitAddress

Because the addresses can be generated offline (i.e., on a computer not connected to the internet), this is one of the most secure methods for storing bitcoins.

The code is open to review, including review by security professionals and improvements to the code have already been made as a result.

I suspect this code can end up getting used as a low-tech merchant point of sale solution as described here:
 -http://bt.irlbtc.com/view/43496.msg538311#msg538311