UV mapping is the 3D modeling process of projecting a 2D image to a 3D model's surface.
This process projects a texture map onto a 3D object. The letters "U" and "V" denote the axes of the 2D texture because "X", "Y" and "Z" are already used to denote the axes of the 3D object in model space.
UV texturing permits polygons that make up a 3D object to be painted with color from an image. The image is called a UV texture map, but it's just an ordinary image. The UV mapping process involves assigning pixels in the image to surface mappings on the polygon, usually done by "programmatically" copying a triangle shaped piece of the image map and pasting it onto a triangle on the object. UV is the alternative to XY; it only maps into a texture space rather than into the geometric space of the object. But the rendering computation uses the UV texture coordinates to determine how to paint the three-dimensional surface.
In the example to the right, a sphere is given a checkered texture, first without and then with UV mapping. Without UV mapping, the checkers tile XYZ space and the texture is carved out of the sphere. With UV mapping, the checkers tile UV space and points on the sphere map to this space according to their latitude and longitude.