Modeling is the process of defining the surface volume of a mesh. Modeling falls generally into two categories: poly modeling and nurbs modeling. Poly modeling is most commonly used in games and simulations whereas nurbs modeling is typically used for engineering and rendering. Nurbs modeling has begun to fall out of favor as poly modeling tools become more powerful. Poly modeling refers to polygons.
A polygon is a closed plane made up of three straight edges (loops) and angles. The point at which edges connect are vertices (three at minimum per polygon). Other shapes commonly referred to as polygons include quads and n-gons so named for their number of sides ("n" being a variable number equaling 5 or greater).
This sphere is made up of n-gons (5 sided polygons)