The Box projection is an extension of XYZ To UVW mapping - the projection of the planes of the cube are based on the normal direction of the surface. Box projections provide a quick way to map a Texture on any object without too much distortion. However, the seams between the Box's projection planes may be visible in the render, depending on the surface's shape (figure 1).
Figure 1: Box projections
Figure 2 shows the Box projection applied to an OctaneRender® Checks texture node.
Figure 2: The Box Projection type