Hi Terry,
After a lifetime of searching for knowledge and learning about different wood, even if one studies wood structural engineering in any university, one will never learn as much about wood until one reads books about either making fine musical instruments or building boats with wood planks.
Quarter sawn lumber is lumber taken from round logs that was sawn in pie shaped quarters, and after cutting into planks, on the wide side of the plank, one can actually count the tree's dark annular rings in a piece of wood.
In laymen's terms, vintage musical instrument makers years ago described wood as having strong, dark annular rings, (very slow growing winter wood) which provides the wood's "strength" ....... and lighter colored annular rings, (larger and faster growing summer wood rings), on each side of the winter wood, to support the thin "stronger" darker winter wood.
Tops of very fine vintage guitars, mandolins, violins etc., made by quality vintage luthiers were always "quarter sawn", where the dark grain annular rings are perpendicular to the very "thin" tops of these instruments to render maximum strength to support the weight or forces coming from the multiple tight strings through the vertically positioned bridge.
For increased strength, and less warping and cupping, select wood flooring is quarter sawn, again to allow the dark grain annular rings to be as near to perpendicular as possible to tops of flooring surfaces.
Flat sawn wood, opposite from quarter sawn wood, can be identified where the dark annular rings, (winter wood), is not very near to perpendicular to the wide surface of the planks.
Just a very short laymen's version trying to simplify quarter sawn wood ... hope this helps.