When the cable housing ends, there is this thin freely mobile plastic covering over the cable. What the heck for?

See photo.

For the lulz

Usually it's remnants of a housing liner or a decorative covering. Nothing to worry about.

Way to spoil it Jeff

You were expecting the Spanish Inquisition?

No one expects the spanish inquisition!

It's the 'straw' the Rats use to inhale cocaine through - as they pull your bike down the road. You'll need a tiny whip.

Sometimes it's part of a sytem used to keep wet grit slung onto the cable from leaking it's way into the cable covering. Usually the ferrules have little nipples that the cover slides onto. Looks like yours might have been a half azzed attempt to do the same.