This is how I think the numbers through when I'm constructing matrices for POV-Ray. This is the order of transformations that is most common in modeling software. If the vectors are not all perpendicular, then the result is a sheared object. A normal cube and a sheared cube. All of the tranforms commonly used in POV-Ray are converted to the matrix form internally.
Translation is the simplest of the transforms to understand.
It simply moves the object. Rotation spins an object around the three axes. POV-Ray expects a vector as the argument for rotation, and so the supplied vector actually provides for three separate rotate actions. The easiest shear matrix to construct works by shifting the object by a certain amount for every unit amount moved along one of the axes. This is how the sheared cube above was produced.