What is the 'meaning' of nowhere dense set? In some books, nowhere dense set is defined to be $int(\bar A)=\emptyset$ but meanwhile is defined to be $int(A)=\emptyset$ in some books(e.g. Munkres).
So what is the 'meaning' (i.e motivation, intuitive/geometric meaning etc.) of nowhere dense set? Thank you.

A set $A$ is nowhere dense if every nonempty open set contains a nonempty open set which is disjoint from $A.$
