At the moment you probably have a copper telephone wire bringing your phone and broadband into your home or business. Broadband delivered through a copper wire means you may get patchy and sometimes very poor coverage, especially if you live a long way from the green cabinet box. In comparison, full fibre means a fibre cable all the way into your house which will give you the fastest and most reliable broadband on offer. Many internet companies may already advertise a broadband package as fibre; however this is most likely to only be a fibre cable to the cabinet and a copper wire to your house/business.
The video below helps to explain why you may want to switch to full fibre - click on the video to view a larger version.
Credits to Superfast Essex for the production of this video.