The report says that to enable higher PPI displays on smaller sized AMOLED panels. The new display panels will use hexagonal and diamond-shaped pixel layouts. Imagining it in your mind's eye, you could see how this would enable more pixels to be packed into a display than the the standard square-shaped pixels.
The reason this move would need to be made if Samsung wanted to up pixel density is that it's been said that 440ppi is the densest that can be achieved with a standard side-by-side pixel layout on a "comfortably sized screen," meaning around 5-inches or greater. To put this sort of PPI on a smaller device would, as things go, require the new system.
It's unclear if the GS4 will sport this setup, but reports of a 440PPI Galaxy S IV have been floating around for a while, so it would seem that, at least, can be expected.
Considering that Apple has long touted its Retina (trademarked) display as 326 PPI or greater, it's unclear that the extra pixels -- a little less than one-third greater density than that 326PPI -- can even be seen. Apple's claim of a Retina display is that the human eye can't discern anything greater than 326PPI.
The GS4, if it achieves 440PPI, wouldn't be the first smartphone to reach that density. Sony’s Xperia Z and HTC’s Droid DNA both have 5-inch 440ppi displays, and the DNA has already shipped.
It appears there is a pixel density war going on.