4k wallpapers are for display devices with 4.000 pixels horizontal resolution.

4K has become the common name for ultra-high-definition television (UHDTV), although its resolution is only 3840 x 2160 (at a 16:9, or 1.78:1 aspect ratio), which is lower than the 4K industry standard of 4096 x 2160 (at a 19:10 or 1.9:1 aspect ratio). wikipedia

So basically a 4k wallpaper is a wallpaper with 3840 x 2160 pixel resolution 🙂