It is very important to add that when it is settled which block of transfers are to be written to the blockchain, one cannot simply put any transfers in the block. Every node actually checks if all transfers are valid. Meaning they check if the source address has the funds to be transfered to next address. With one single exception, it is allowed to make one sourceless transfer of a defined amount, which currently is 25 bitcoin, which is how bitcoins are created.

In bitcoin, what a person actually have are you account (called public address) and the password to that account (private key). The private key allows you to transfer any coins that were transfered to the corresponding public address to another public address. So as long as you have a copy of the private key you have access to the coins. If you only have a single copy of the private key in a flashdrive and than it is destroyed you will lose the coins. Obviously you make some copies of the private key to be safe of that possibility.
By now I suppose you can see why you cannot simply copy bitcoins. You can copy the key, but the key only gives the bearer access to the coins in the address.