Mute is one of the social features that Hive have (most Hive frontend DApps honor muting).
Any account can build a list of other accounts that don't want to see the account’s posts and comments. A list of muted accounts can be followed by other accounts, which means anyone following a mute list will not see posts and comments of all accounts inside that list.

There are not so much story, explanation, theory about mute feature, is a tool that anyone can use and like the name say, to not see/read someone around Hive. I admit that it can be a very useful and healthy tool for those who suffer from some kind of bulling, for example.