With the bottom row flipped on end, it allows you to stack two more bales per row and use the space more effectively. In our barn, I usually flip the bottom 7, set 7 on top of those, and then 6 on top. If you were stacking them without flipping, it would be 7 on the bottom, 6 middle, and 5 on top.
It really only works well on bales that are pretty square, about as tall as they are wide. You wouldn't be able to do it with 6x4s, too much space between the rows and they would shift and lean over. I have that problem with our 5x4s at times.
If you have pallet forks, you could stack 3 rows on end, but I can't imagine getting them back down would be all that easy.