You don't see it but you're client makes a random private key which it uses both to make the public key (that you see and share) and to spend any coins sent to that address. People could only pretend to be you on the receiving side, which would mean free money for you.
but what If I want to use it on several computers?? or what if I have to reinstall windows n stuff? seems very weird/impractical.
You can run bitcoin on another computer, it'll get a new address and send bitcoins back and for between the addresses.
Or copy over your wallet.dat to the other computer and you can use the same accounts.
As for reinstalling Windows: that would be the same thing as every other document on your computer: if you don't backup your Word documents before reinstalling them for instance, you will lose them.
Take a look at the
wiki to see where your wallet.dat is stored and how to back it up.