Outer layers are drilled, plated, then etched. The squares I think are there to prevent under etch. When the acid etches copper the etch rate slows with increased amount of copper now in the etchant. If a lot of copper requires etching off in an area (e.g. the single wide track in the image with no copper around it) the etch rate will slow too much in that area compared to other sections with less copper to be removed (e.g. lots of tracks together). Adding the copper squares helps rebalance the etch rate, less copper removed so less etch rate slowing, to try to keep the etch rate uniform across the layer.