4k
4k (aka UHD or 4k UHD) is the term for a screen resolution of approximately double that of Full HD in both directions (four times the Pixel count of Full HD).
It name derives from the 4,000 rows of pixels commonly used in Cinema. Since today's TFT displays are in a 16:9 layout and for simpler upscaling the most common resolution on a PC is 3840 x 2160 pixel - instead of 4096 x 2160 in an un-cropped Cinemascope movie (1.9:1). As of 2015 more and more television sets and PC monitors supporting an UHD resolution are available.
The next higher resolution would be 8k, effectively doubling both X and Y resolutions another time, featuring eight times the pixel count of Full HD.
PC
The first PC graphics cards that were powerful enough to support 4k output were introduced around 2015.
PlayStation 4 Pro
Unlike the original PS4, the PlayStation 4 Pro is able to display games that were specifically enhanced for this system in 4k resolution. It was introduced on 7 September 2016.