The place where two streets or lines cross eachother.
The point at which two lines (or curves) touch, even if the lines/curves do not cross each other, is called their intersection. The lines (or curves) are said to intersect at that point. So, the corner of a rectangle is a point of intersection of two of the sides. Intersecting lines are lines that share a point in common (or, less commonly described as "intersecting," coincide entirely).
See multiplication for more about how the intersection model is used in Think Math! along with the area model.
Vedic mathematics, from India, uses an intersection model for multi-digit multiplication. See video on Vedic multiplication.
What's in a word?
inter- (between or among, mutually or together) + -sect (cut) = "mutually cutting"; two roads "cut" (across) each other at their intersection.