Definition of "Intersection" :

noun: the act of intersecting (as joining by causing your path to intersect your target's path)

noun: a junction where one street or road crosses another

noun: a representation of common ground between theories or phenomena

noun: a point where lines intersect

noun: the set of elements common to two or more sets

"The set of red hats is the intersection of the set of hats and the set of red things."

noun: a point or set of points common to two or more geometric configurations