It is often used to describe something that is done to the greatest extent possible. For example, someone who has gone "Full Williams" in training is pushing their body into working out to the highest level of intensity. It can also be used to describe someone who is intensely committed to a new hobby or interest. Someone may be described as Full Williams if having walked into a camera shop, with the intention of buying a new compact camera for family snaps, they subsequently leave with a top of the range SLR setup, complete with an array of Lenses, Filters, lights, reflectors, and associated paraphernalia.
Jesus have you seen Johns new bike? He's only been on two bike rides and he's just spent £5k on a carbon fibre road bike and full Rapha setup, Yeah he's gone "Full Williams" on that one!