4K, or UHD, refers to a resolution (usually) of 3840 x 2160 and (again, usually) 60 frames per second. To put another way, 4K is four times the resolution of standard HD (which is 1920 x 1080), and is always progressive, rather than interlaced.
Are 4K TVs progressive or interlaced?
These factors are the other important goals defined in the ITU-R's (aptly dubbed) Rec. 2020 spec for 4K/UHD. Namely, they are (larger) color space and (progressive-only) frame rate. The official spec is properly called ITU-R Recommendation BT.
Is 4K 1080i?
Your 4K TV has a resolution of 3,840x2,160 pixels. Pretty much all cable, satellite, streaming, gaming, Blu-ray and other video content is 1,920x1,080 pixels (which is called 1080p and 1080i) or 1,280x720 (called 720p). All 4K resolution TVs have four times as many pixels as 1080p TVs.