It is very simple. It is a player who plays with their head. I don't mean that they are good in the air. I mean that they think about the game. Now this is not as obvious, as it seems. It is quite possible to be a gifted footballer and to never think about what you do, on the pitch. You can be the best player in the team and be as dumb as a box of hair. If that is the case, then you are not a Scotch Professor.
Why are they called Scotch?
They were given that name in the 1870s, when northern English clubs started paying Scotsman to head South. Their job was to teach the Scotch professor passing and running game to clubs like Preston North End, Blackburn Rovers, Blackburn Olympic, Aston Villa, Sunderland. . It showed that they were playing a cool, intelligent code of football, which was unknown in England.
Surely this name is unfair to people who are not Scots?
The first players from Scotland were the original Scotch professors. However: it is a state of mind. It is a way of thinking. Here are some Scotch professors: Johan Cruyff, Jose Piendebene, Diego Maradona, Hugo Meisl. What is the link? None of them are Scottish, but all of them can trace their ideas on football back to the Scots who travelled the world, bringing the passing and running game to everyone who wanted it.