What is the difference between a convex and a concave polygon?

A polygon is a closed plane curve made up of straight line segments. If the curve is not self-intersecting, that is none of the line segments cross each other then it is a convex polygon or a concave polygon. The way to tell the difference is that if you pick any two points in the polygon or on the boundary lines, and connect them with a straight line, the straight line may or may not go outside the polygon. If it stays inside between the points the polygon is convex, if it intersects the boundary and goes outside the polygon then the polygon is concave.