What do School League Tables Really Tell Us?

As a private tutor I am often asked for help 'to make sense of' the barrage of facts thrown at my tutees by their teachers in class.  The majority of my tutees come from schools 'high up' in the league tables.  I believe this to be the case with many other private tutors.  After private tuition a student's grade may often increase by two or more yet it is the school that gets the credit for this in their position in the league tables. Hence my original question: 'What do School League Tables Really Tell us?'  The fact that private tuition is the largest growing business says it all.