The spinner spiral was normally a feature only found on FRONT LINE units (ie, war fighting units)... Its main purpose seems to be to show that the a/c was from one of these operational units (and in fact in some cases, you can tell what Jagdgeschwader an a/c is from by the style of the spinner spiral), but also has the added benefit of being a visual indicator that the a/c prop is spinning (hence its use on modern a/c - turboprops on carriers and moste every turbofan I can think of), so when you're ground crew is running round in all the noise and dust and smoke, they can see that a prop is moving!
Additional stories Ive heard is that frm head on, it makes aiming at the a/c harder; but I dont really see how this works, as closing speeds wouldnt give you time to really be affected by this...
But yeah, in summary i) defines the a/c as being from an operational, front line unit and ii) provides a visual cue to the fact a big, head splitting lump of steel or timber is rotating in your vicinity!
Dan