Park City - when a phone is "locked", it is coded to only accept the SIM card for a particular network, in your case Verizon (Vodafone!). If you put another network SIM in it just won't work. To have it unlocked means that you can use the phone on any compatible network by using the SIM card for that network. This has to be done by software/SMS remote programming. It costs unfortunately.
The reason networks lock phones is that they want to claw back their investment in you, the customer. When they offer all the cheap deals, e.g. "look at the super phone from xxxxxxx we can give you" type of thing, they heavily subsidise the cost of the phone. This is why you can get the latest all singing/dancing gizmo for a few dollars instead of the hundreds that they really cost. Hope that helps!
I suspect, but don't quote me on this, that Telecom NZ is on a different type of system than Vodafone. I will have to look this one up. Await further info regarding the texting problems you are all experiencing. It may be due to the SMS platform being used by one or both companies not being set up to accept SMS from the other company. Will have a dig around.
Steve