For example consider the lines and. The theory for varieties is older with roots in Bezouts theorem on curves and elimination theory. In math an intersection is the spot where two lines cross.
In mathematics intersection theory is a branch of algebraic geometry where subvarieties are intersected on an algebraic variety and of algebraic topology where intersections are computed within the cohomology ring.
In the figure above we would say that point K is the intersection of line segments PQ and AB. The point of intersection of two curves is significant in that it is the point where the two curves. Point of intersection means the point at which two lines intersect. Another way it may be said is that the line segment PQ intersects AB at point K.