This comment can be seen very often on Japanese message boards.
KY is short form of 空気読めない (Kuuki Yomenai)
KY means being unable to read the situation or being unable to pick up on the mood of a conversation.
It means kuuki yomenai. A friend explained this concept as follows:
In Japanese culture, the social protocol calls for utmost attention to the right "atmosphere." Certain actions can only be considered appropriate when the "atmosphere" of the time and place allowed for them to be carried out. In Japanese lingo, it is "reading the air" (空気を読む）and for every person deemed to be lacking in such skill, the term "KY" ("cannot read the air, "Kuki Yomenai," 空気読めない) is ruthlessly (albeit sometimes jokingly) applied. The presence of these KY people is definitely a source of massive awkwardness and discomforting bluntness in any social gathering, whether work-related or otherwise.
Well, being careful to avoid KY-ness is obviously of high importance in certain work conditions. In the presence of one's superiors, or worse, external guests, doing anything KY, i.e. making overly argumentative comments against the others, aggressively doing something that should be reserved to the superiors, and so forth, as a new graduate, is bound to be highly humiliating and irritating for the superiors.
Sadly, one common example of KY is when leaving work. Unless you avoid KY, it will be considered rude for you to leave work, but of course this depends on the environment.