This came from Wikipedia:
https://en.wikipedia.org/wiki/Korean_War#Names
It has been referred to in the Anglosphere as "The Forgotten War" or "The Unknown War" because of the lack of public attention it received both during and after the war, and in relation to the global scale of World War II, which preceded it, and the subsequent angst of the Vietnam War, which succeeded it.
I don't get the impression that the Korean War is very forgotten, although I may be biased by living in an area full of Koreans. I seem to get reminders from CNN about how the North-South split happened all the time. And I haven't heard anything about the Vietnam War in pop culture since Tropic Thunder, so how is the Korean War the most forgotten of them all?
I would definitely agree with the sentiment that the korean war is one that gets a lot less mainstream attention.
I can only speculate on the reasons. One, it's overshadowed by WWII before it which was so much more grand in scope and by Vietnam after, which was significant because people more or less agree it was a grave mistake. Vietnam also gets more attention because of its parallels to more recent interventions like the invasion of iraq.
I also think that since there was no clear winner, its lessons weren't as easy to understand.
David Halberstam's "The Coldest Winter" gives a great overview of the war and he also highlights why he thought it was an important conflict in our history.