4k is simply a resolution, 4096 × 2160 pixels. consumer 4K is more correctly refereed to as UHD which is 3840 × 2160. (double FHD)
in order to run 4K graphics, you need a GPU that can Handel those resolutions, a link interface between the GPU and the monitor that supports 4k, and a display that supports 4K signals. Netflix, Amazon, and YouTube currently support delivery of UHD media. supposedly there's a physical disk medium in the works for UHD media also.
as of right now, Display Port is your best bet for UHD and higher resolutions, as only Nvidia's Maxwell GPU's have HDMI2.0 which is needed for proper 4k/UHD resolutions over the HDMI standard.