Definitions 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 point where lines intersect
• noun:   the set of elements common to two or more sets

  Example: "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
• noun:   a representation of common ground between theories or phenomena