The explanation is already given in the page:
No subtle put-downs or unfriendly language.
Even if you don’t intend it, this can have a negative impact on others.
Some examples are also given in tabular form:
See here both messages on left side and right side are illustration same things being said with different tone.
There are three styles of communication. (Let's take one example of communication between A and B). I'm not expert in such topics related to communication skill, however I think it may be useful and related to write here.
A express his thoughts with hostile tone and tries to impose B's statement are false and thinking I (A) am only saying true. This is also called winning condition (I win, you lose). A doens't care about feelings or rights of B.
A express his inner thoughts in passive (indirect) way thinking himself powerless or resentful. Considering B superior to him. (I lose, you win).
A is conveying his thoughts without hurting feelings of B and also not thinking B is superior to him) This is the healthy communication born of high-esteem. (I win, you win)
For healthy and constructive communication, assertive style of communication is recommended. You can learn the difference between these style with examples of behavioral characteristics, language etc. from this article.
I think StackExchange recommend to use the tone/language that is of assertive style, clear, open, constructive, honest and doesn't impact negative effect on others -- that can be called friendly.
It may be the case that although we are not intentionally demeaning or criticizing the post or poster, the choice of improper language may negatively impact like we're talking so i.e demeaning or criticizing. So, in order to avoid such misunderstanding or misconception, Friendly language is to be followed and Unfriendly tone should be avoided. This is very useful especially while communicating with new users. With the similar idea New Contributor Indicator is recently implemented.
So, if you find that unfriendly (criticizing, negative, hostile or aggressive) language in comments, you can flag appropriately.
I'll add some examples if needed.