I'm not totally sure how someone even takes ownership of a bitcoin. How does the data exist and is it tied to the hardware it currently resides in? I just read the story of James Howell and how he threw away a hard drive that contained 7,500 bitcoins. Could he have backed up the data on multiple hard drive to make sure he always had the data for the bitcoins? I read that passwords are involved and that a private key is the way to make sure you maintain ownership.
Can someone explain it to me?
Basically, the bitcoin network contains a sort-of ledger that's distributed between all participants in the network. Say you have a bitcoin, and you wish to give it to your friend. In order to do that, you have to register with the ledger that you wish to transfer that bitcoin. In order to register that transfer, you need to use a private key that only you know about (the principle here is identical to public key cryptography, which you can look up on wikipedia for more information).
Those bitcoins that guy lost still exists. They're registered in the massive, distributed bitcoin ledger to his account, whatever it was. But since he lost that hard drive, he lost his private key, so he can't do anything with them. It's like having a million dollars locked up in a safe you can never open.
So yes, if he'd backed up his hard-drive, he'd still have his private key, and thus access to all his bitcoins.