Any question answered...

How does unlocking a phone off a network work?

In the past I've bought a code off eBay. But what actually happens?

At a guess network locking is at a firmware level and the phone runs a bit of code that requests the firmware remove the lock, at which point the code is required, and the O/S or whatever supplies the code and the firmware updates itself to the unlocked state should the code match whatever algorithm the firmware uses to identify valid codes.