Full Fibre Broadband is another term for Fibre To The Premises (FTTP). Rather than having a fibre connection that runs to an exchange close to your premises and then copper cabling connecting you to the exchange, the fibre connection runs directly to your premises.
The advantage of this is that you gain access to faster speeds. This is because copper cables intended initially for phone calls reduce your bandwidth (speeds), whereas fibre cabling can have much higher bandwidths.