Specifically, what is the meaning of affaire in this sentence?
I would aim at “It is everybody's business”.
Affaire in this context means “stuff one should be interested in”, it is not related to commercial activities (unlike, for instance, in homme d'affaires, which means businessman)
Affaire generally corresponds to “business” in the sense of something that somebody should be concerned about (the kind of business that one minds).
Affaire is broader than “business” in this meaning, it can more generally mean something that is happening and is a concern of some kind.
The word affaire has many other meanings, including some other meanings which can be translated as “business” in the economic sense: