A polygon is a closed twodimensional shape. It is also a simple curve that is made up of line segments. It usually has three sides/corners or more. It could also be referred to as 'A closed plane figure bound by three or more line segments'. It has a number of edges. These edges are connected by lines. A square is a polygon because it has four sides. The smallest possible polygon in a Euclidean geometry or "flat geometry" is the triangle, but on a sphere, there can be a digon. The monogon is a theoretical figure that cannot exist  it has only one side and one edge.
If the edges (lines of the polygon) do not intersect (cross each other), the polygon is called simple, otherwise it is complex.
In computer graphics, polygons (especially triangles) are often used to make graphics.
Images for kids

The Giant's Causeway, in Northern Ireland