3D models typically start with the creation of a mesh. Most 3D software allows for a mesh to be viewed in a wireframe mode, which allows the user to see the lines and vertexes that create the 3D shape. The mesh contains important data that computers use to properly render the 3D model. Thus, polygons become a natural necessity due to the nature of how meshes are created and used in real-time. This is also an advantage 3D has over traditional art forms because a mesh can be animated and changed in real-time non-destructively.
A 3D mesh is a net of polygons, connected by lines and vertexes. Alone, a polygon is just a 2D shape made up of at least 3 vertexes and lines, also referred to as edges. These points joined together create faces, often referred to as triangles, quads or N-Gons depending on how many vertexes and edges form them. In 3D modelling, N-Gons refer to any polygon that has more than four vertexes and edges and should be considered undesirable. Good topology practice recommends the use of tris and quads only for the cleanest results.
Polygon modelling is considered the standard for 3D modelling due to its adoption in nearly every commercial 3D software. It is used to create 3D meshes with accurate and deliberate topology. Polygon modelling is preferred in VFX and gaming especially. Because gaming often requires many assets to be rendered in real-time at once, developers must be mindful of polygon counts in relation to hardware constraints. Different consoles and PCs will all have varying limitations as to how much they can handle. Thus, 3D artists who work in these spaces, prefer polygon modelling due to the heightened control they have over each model.