If you don’t know the story:
As I was told, three soldiers were in a strange village, and none of the villagers would share any of their victuals. So the soldiers asked for a large pot, and began boiling stones. The villagers became curious, and the soldiers said they were making stone soup… "But it would be so much better if only we had some potatoes to put in, like we make it back home." And a villager, curious about stone soup, runs off and gets some potatoes. And the story goes on, adding different ingredients, until they have a huge pot of rich soup which they share with everyone, and all agree it was the best soup they ever had.
So, the use of the stone is to recall the familiar story of community and sharing, a cultural touchpoint.