Kella Knack on the Altium website has a very detailed explanation on the "The History and Use of Cross-Hatched Planes" which summarizes some of the previous responses.
She says "In the earlier days of the multilayer PCB fabrication process, the final step of inner layer processing involved roughening the copper surfaces so that they would adhere tightly to the resin in the prepreg system during lamination. This step was necessary because the copper surfaces as they emerged from the DES (develop, etch, and strip) process were very smooth. In fact, they were so smooth that it was difficult to create a strong bond between the resin used to laminate the PCB and the copper. As a result, if the copper surfaces weren’t roughened, delamination would occur between the laminate and the solid copper planes of the PCB. This same problem occurred with component mounting pads on outer layers resulting in pads coming loose from the PCB while soldering during rework." ... "To address the foregoing copper adhesion problems on rigid multilayer PCBs, cross-hatching was created. The actual process involved creating small openings in the copper plane so that the resin would bond to the laminate through the copper, rather than attempting to force a bond directly between the resin and copper."
As to why it is still used today, she says "while cross-hatching is rarely used in rigid PCBs these days, it does have practical application for both flex and rigid-flex circuits" ...
Controlled impedance in flex regions: Using a hatch ground is a good method for providing the reference plane required in controlled impedance routing for high speed digital boards." ... "It should be noted that cross-hatching reduces the amount of copper under a transmission line, which decreases the capacitance and raises its impedance." This allows for more trace width/spacing options when dealing with controlled impedance which is useful for rigid PCBs as well.
"Structural support for flex regions: Using a hatch ground provides structural support needed for a dynamic or static flex ribbon without increasing the rigidity of the copper layer. on a two-sided flexible circuit. The layer can still be used for controlled impedance routing creating undesired rigidity, or the ribbon can be permanently deformed."