That's a great question and it comes as a surprise to many people that there's no one official answer, but the three main organisations involved in driver training have come together in an attempt to define standards.
Motoring groups, such as ROSPA or the IAM (Institute of Advanced Motorists) had their own interpretation of what advanced driving is for some time, but have now issued a joint statement with the DVSA.
"Advanced driving is the ability to control the position and speed of the vehicle safely, systematically and smoothly, using road and traffic conditions to progress unobtrusively with skill and responsibility. This skill requires a positive but courteous attitude and a high standard of driving competence based on concentration, effective all round observation, anticipation, and planning. This must be co-ordinated with good handling skills. The vehicle will always be at the right speed with the correct gear engaged and can always be stopped safely on its own side of the road in the distance that can be seen to be clear."
- DSA, RoADAR, IAM, 1997
That definition is quite a mouthful. No doubt each of the groups involved in it's conception needed to ensure that their most promoted indicators of Advanced Driving were incorporated into it. Never the less, it's a very good definition and it does make complete sense. It also makes sense that the major organisations agree on a standard.
There are still differences between these organisations, and make no mistake, members of these organisations still disagree over various aspects of Advanced Driving.
ROSPA provide a much simpler version in the last paragraph of their test guidelines document:
"The hallmark of an Advanced Diver is to always be in the correct place on the road, travelling at the right speed for the circumstances and with the correct gear engaged. It is that simple"
ROSPA Advanced Car Test Guidelines For Candidates And Tutors, 2016 (available from the ROSPA website)
It would be difficult to imagine a more concise statement.
With my experience of both the IAM and ROSPA, it is my opinion that the ROSPA test is the closest to actual Police driving. Passing the ROSPA test at 'gold' standard is still widely regarded as the highest level of driving qualification open to the public.
If you want to become a better driver I would urge you to consider joining either ROSPA or the IAM. You may even be able to get a basic level of training for free or for very little outlay.