UV texturing permits polygons that make up a 3D object to be painted with color (and other surface attributes) from an ordinary image.
The rendering computation uses the UV texture coordinates to determine how to paint the three-dimensional surface.
On the left, without UV mapping, the sphere is carved out of three-dimensional checkers tiling Euclidean space.
A UV map can either be generated automatically by the software application, made manually by the artist, or some combination of both.
Often a UV map will be generated, and then the artist will adjust and optimize it to minimize seams and overlaps.
If the model is symmetric, the artist might overlap opposite triangles to allow painting both sides simultaneously.