But, no one has ever been able to show me where it really matters.
It just shows if holders are selling or not.
Most of the volume comes from traders who will sell if it price goes up.
When thousands of days are destroyed, we have a movement of selling which is deeper than the usual, when true holders are selling.
It also can prevent fake volumes, like the smart person sending coins back and forward.
I don't think it is an useful metric... but that is it.
From the nc50lc link:
The idea of "bitcoin days destroyed" came about because it was realised that total transaction volume per day might be an inappropriate measure of the level of economic activity in Bitcoin. After all, someone could be sending the same money back and forth between their own addresses repeatedly. If you sent the same 50 btc back and forth 20 times, it would look like 1000 btc worth of activity, while in fact it represents almost nothing in terms of real transaction volume.
With "bitcoin days destroyed", the idea is instead to give more weight to coins which haven't been spent in a while.