NAT is a way of translating one internet address from your BB supplier into any number of different addresses for your local network. When a pc wants to use the internet, your router translates the pc's network address into the internet address in such a way that, when a reply comes, it knows which pc to send the reply to.
This saves internet addresses, otherwise every pc on every network would need an internet address and soon there would be none left.
NAT is carried out in your router, not by BT, and it is unusual not to have it enabled.
Why do you want to turn it off?