I have annotated the game Apsenieks - Maroczy, Folkestone 1933, which I came across the other day in the book of the 1933 Folkestone Olympiad. It offers a great illustration of how an advantage in piece quality (including scope, piece safety, and coordination) can lead to victory.
It was in R.N. Coles's book Dynamic Chess where I first came upon the idea that chess is a game of four dimensions: material (based on the relative value of the pieces), time (development and initiative), space (control of the board), and position (meaning structural or dynamic weaknesses and strengths in your pieces, pawns, coordination, or king safety). Players typically understand them in that order, with what Coles called "position" (and which others have termed "quality") the hardest to master, just as it was historically the last to gain widespread recognition among theorists. That's why I only lecture to my young chess students on "time, space, and the material world," since those three abstractions are enough of a stretch. When they are ready for the fourth dimension, they will be ready for chess mastery.
At a certain point, mastery of the game involves combining the four dimensions so that all become inter-related, exchangeable, and fungible. That's why the four are often reduced in recent formulations. In Kasparov's view, there are really only three dimensions to the game: material, quality, and time. Robert Huebner has deconstructed Kasparov's three to show that they all really reduce to "quality" in the end. And Jonathan Rowson (who reviews their work in Chess for Zebras) argues that practical players need to acknowledge the critical role of the chess clock (always ticking), so that he adapts the Kasparov model to make "material," "opportunity" (his rendition of Kasparov's "time"), "time" (meant literally), and "quality." I think Rowson makes a good case, especially since at no other time has the clock played such a significant role in the game. But whether they see chess in one, three, or four dimensions, everyone seems to agree that the concept of "position" or "quality" is the most crucial.
In his discussion of "quality," Rowson breaks it down into safety, structure, and scope. Most beginners understand the notion of king safety soon enough, and they learn to understand and use pawn structure. But the concept of piece quality or scope takes a while longer to recognize because it is so dynamic and less visible than a broken castle position under assault or doubled pawns under restraint. In a sense, scope is less inscribed in the pieces themselves than it is in the force-fields that they radiate. So piece quality is not something you see until you are used to seeing your pieces less as objects than as actors.