i heard it has something to do with cold wallets and offline wallets and bitaddress.org. My question is how do you create an address without ever being online? How does the network know or recognize your address?
The network doesn't need to know or recognize your address. Addresses are something we humans use to make it easier to use the bitcoin protocol without understanding the technical details.
At the protocol level (in the transactions and the blockchain) there aren't actually any bitcoin addresses at all. That is just something that websites and wallets show us so that we don't need to understand the technical details of what is actually happening.
There is software that can run offline (bitaddress.org is just one example) which can generate a private and public ECDSA key. Then the software can perform the proper hash functions on the public key. The result of these has functions is a value that can be used on an online wallet to "send bitcoins". The blockchain is then updated with a transaction that assigns a value to an output and requires that certain conditions be met before that value can be re-assigned anywhere else.
The main requirement for most bitcoin transactions is a digital signature generated with the private key that is associated with the hash value that was used in the transaction. In the case mentioned above, the private key was generated and stored offline. Therefore, the private key is not (and has never been) accessible from any computer that has ever been online.
This means that the only person (or people) that can meet the necessary conditions to re-assign the value elsewhere is the person (or people) who have physical access to the private key that was generated offline.
