Quarter sawn is done with the saw on the radius of the log. So you get wedges of whatever size you want, then plain them down to desired flat boards.
Usually logs are turned into boards by simply starting at one side and sawing off parallel boards rite across the entire log. In quarter sawn, the center of the original tree is one edge of each board. I think the main advantage is visual, but there may be some strength advantages. The stock for violin family backs and tops is always quarter sawn. tom fowle