The term "intersect" means to meet, cross, or overlap.
Lines, rays, line segments
The blades on the windmill represent line segments that intersect or meet. When two lines, rays, or line segments intersect, they have one common point; in this case, the line segments intersect since they meet at the center of the windmill's blades.
In the figure below, point (3,4) is the intersection of line x = 3 and line y = 4 since that is where the two lines cross. The point can be located by starting from the origin then following the red arrows on the grid.
Other geometric figures
Some geometric figures intersect at more than one point.
When two distinct planes meet, they intersect at a line.
When a plane and a sphere meet, their intersection forms a circular section.
In the diagram above, plane p intersects a sphere with center O forming a circle with center O. The circle is called a great circle of the sphere since it contains the center of the sphere.
It is also possible for sets to intersect or share common elements. The Venn diagram below shows the intersection of multiples of 2 and multiples of 3 within the set of whole numbers from 1 to 12.