right well this is from photography/art.
the rule of thirds, or more complexly the Golden Mean/Section is essentially a mathematical principle- a universal constant to do with aesthetics.
a/ lets say you have a piece of paper. you draw a tree right in the middle.
b/ same as above, but using golden mean you calculate where the tree should be placed on the page. it will, theoretically always be more pleasing to the eye when it is placed off-centre.
Its loosely called the rule of thirds, because the most aesthetic way of diving the page tends to look approximately like it is 2/3 in. If you look at the composition of most of the clips from AvPR, the actors, buildings or foregrounds are usually 2/3 in the frame. Or the frame is divided in thirds al around. Mild "abstractions" is simply a quick way of saying "cropping the environment/background of the frame so that it looks as pretty as possible- almost like a pattern."