A Bitcoin address is equivalent to a random number. The possible numbers this random number is picked from, is such a huge range of numbers (possibilities are as large as a 1 with 26 0's behind it!) that we can just pick any number in there and have almost the same odds of picking the same number someone else did. (If I tell you to pick a number between 1 and 10, you have a 1 in 10 chance of picking MY number.)
Meaning that, if I have a computer not connected to the internet, it can still pick a random number and create a human readable bitcoin address corresponding to the random number and be pretty sure that number / address has never been used before.
This is a really great part of the system, because now I can send bitcoins to the address I just generated, knowing that I have the password (Private Key) for that address, but no one will steal that password, as long as my computer is not compromised (and it won't since it isn't connected to the internet.)
Also, every bitcoin address is permanent, since once it is included in the blockchain, it won't ever disappear out of it. The only thing you can lose is your private key. But the address will be included in the blockchain for as long as the blockchain will be run.