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No, it's not tied to your IP, it's tied to your wallet.

When your client generates an address, it first generates a key (called a 'private key'). It then generates a lock that only your key fits (which is not exactly the same a public key, but very similar). The address is the lock, not the key. You give other people the lock so they can send coins that you have the key to. You never reveal that key to anyone, and it remains in your wallet.

The mathematics that make all this possible are quite amazing actually. If you want to learn about them, I'd start with this:
http://en.wikipedia.org/wiki/Digital_Signature_Algorithm
It's not the same algorithm that bitcoin uses, but it's very similar and much easier to understand.

thanks for the help - i think im confusing wallet address with the wallet file and it sounds like i was correct in guessing (above your first post) that it has to do with the wallet "file" on my pc and having the wallet address doesnt matter - correct?? (so i cant use my bitcoin address on another computer if i wanted to for example)

Quote from: senbonzakura on July 16, 2011, 05:43:49 AM

done i sent you 2 bitcents to your address. For small amounts of btc you can use instawallet, it gives you an online e-wallet account to keep your btc in. no need for registration.

wow thanks - my first funds in bitcoin Wink