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.
What is a "permanent" address? – George Kimionis – 2015-01-13T23:04:49.607
one weird thing tho : if I'm not online, how can the wallet be sure that it has not generated a adress already made by someone else? – sliders_alpha – 2015-01-13T23:38:09.817
@sliders_alpha Good question. It can't be sure. However, generally speaking, collisions like this are possible in many facets of the bitcoin protocol and the protocol basically assumes that these events are so improbable that they can be ignored. If you make the public key offline using some kind of secure algorithm (flipping coins to take the extreme example) it is effectively impossible to duplicate another. For example of another kind of related collision, it is conceivable that two different private key could map to the same public key. Again, we just assume this will never happen. – Nick – 2015-01-14T19:21:30.297