To give a really simple answer:
People used to animate textures by changing one of the numbers in the mapping node, maybe rotating the texture in a way that isn’t too noticeable. But on a 3D object a viewer could often tell which way the pattern was moving, and that’s not always good.
This new W number lets you change the number, and therefore the pattern of a texture uniformly across the whole object. So it won’t look like it’s drifting up-and-to-the-left for example.
