It's 4k because it's an HD resolution (1080) doubled horizontally and vertically.
If this is HD:
┏━━━━┓
┃ ┃
┗━━━━┛
Then 4 of these tiled become 4k:
┏━━━━┳━━━━┓
┃ ┃ ┃
┣━━━━╋━━━━┫
┃ ┃ ┃
┗━━━━┻━━━━┛
I used to have 4 separate HD monitors laid out horizontally on my desk, and in terms of pixel realestate, a 4k effectively replaces them... until retina/high density displays became affordable. Now my 5k monitor is effectively the realestate of 4 HD monitors, but nice and smooth.
640x480 (VGA), 800x600 (SVGA), etc came from the computer industry since they had 4:3 CRTs
720p, 1080p came from the TV industry since they always counted video in "lines" (NTSC is 525 lines)
4K came from the movie industry (the 2005 Digital Cinema specification), since movies have wildly different aspect ratios so counting the vertical doesn't make sense (specifically, it's very rare for movies to be 16:9!)
If this is HD:
Then 4 of these tiled become 4k: I used to have 4 separate HD monitors laid out horizontally on my desk, and in terms of pixel realestate, a 4k effectively replaces them... until retina/high density displays became affordable. Now my 5k monitor is effectively the realestate of 4 HD monitors, but nice and smooth.