Balance is the proper blending of the various elements found in a wine including acidity, alcohol, tannins and sweetness. Another way of thinking of this is as the harmonious relationship between acids, alcohol, fruit, tannins, and the other natural elements...
"Balling" is a synonym for Brix - a measurement which generally refers to the amount of soluble sugar solids in grape juice (i.e. to quote Jackie Gleason, "How sweet it is!").