The intangible story of an item is what it represents to the finder.
I know from my personal experience that found items can capture a precise moment in time for the finder, not just in terms of where it was found but also the circumstances of my life at that time.
So often, the object can form a link to a moment in time for the finder that, on a personal level, far exceeds any monetary or historic value in the object. This is truly what we often term as "sentimental value" and is an aspect that can never be fully appreciated by any future owner of the item.
These are a few of mine.