With the introduction of the PS4 Pro is the ability to play games in 4K with HDR. A lot of people will say that the system is unable to handle Native 4k and this is partially true, but also false. It is true, the PS4 is not able to render native 4k, but with checkerboard rendering, it is actually possible to render 4k that may not be traditional 4k, but in most cases people will be unable to even notice the difference.
Essentially, checkerboard rendering is a way upscale a game that doesn’t result in the typical blurring and quality degradation we see with standard upscaling. For the average person, you should not be able to see the fact that this is not native 4k unless you are very close to the screen.
This video will explain how it works quite easily. It explains why it is called checkerboard and how it actually works.