The idea of cube mapping is to store six textures and to visualize them as the faces of a cube, centered and axis aligned about some coordinate system. Because the cube texture is axis aligned, each face corresponds with a direction along the three major axes; therefore, it is natural to reference a particular face on a cube map based on the axis direction (+-X, +-Y, +-Z) that intersects the face.
In contrast to 2D texturing, we can no longer identify a texel with 2D texture coordinates. To identify a texel in a cube map, we use 3D texture coordinates which define a 3D lookup vector v originating at the origin. The texel of the cube map that v intersects is the texel corresponding to the 3D coordinates of v.
The primary application of cube maps is environment mapping. The idea is to position a camera at the center of some object O in the scene with 90 degrees field of view angle (both vertically and horizontally). Then have the camera look down the positive x-axis, negative x-axis, positive y-axis, negative y-axis, positive z-axis and negative z-axis, and to take a picture of the scene (excluding the object O) from each of these six viewpoints. Because the field of view angle is 90 degrees, these six images will have captured the entire surrounding environment from the perspective of the object O. We then store these six images of the surrounding environment in a cube map, which leads to the name environment map.
We can use an environment map to texture a sky. We create an ellipsoid that surrounds the entire scene. To create the illusion of distant mountains far in the horizon and a sky, we texture the ellipsoid using an environment map. We assume that the sky ellipsoid is infinitely far away, and so no matter how the camera moves in the world, we never appear to get closer or farther from the surface of the sky ellipsoid. To implement this infinitely faraway sky, we simply center the sky ellipsoid about the camera in world space so that it is always centered about the camera.
The other main application of environment maps is to model reflections for arbitrary objects. Now suppose that we want animated actors moving in our scene. With a pre-generated cube map you cannot capture these animated objects, which means we cannot reflect animated objects. To overcome this limitation we can build the cube map at runtime. That is, every frame you position the camera in the scene that is to be the origin of the cube map, and then render the scene six times into each cube map face along each coordinate axis direction. Since the cube map is rebuilt every frame, it will capture animated objects in the environment, and the reflection will be animated as well.
Introduction to 3D Game Programming with DirectX11, Frank Luna, 2012