[Mithadan]

My view of how the Standing Stone fits in the story is based upon Tom's explicit warning to the Hobbits. He "advised them to pass barrows by on the west-side, if they chanced to stray near one." The Hobbits ignored or forgot this warning. "It was shapeless and yet significant: like a landmark, or a guiding finger, or more like a warning. But they were now hungry, and the sun was still at the fearless noon; so they set their backs against the east side of the stone" and fell asleep. When they woke, "The standing stone was cold , and it cast a long pale shadow that stretched eastward over them." Having failed to heed Tom's warning to pass such markers to the west, they became ensnared.

One could argue that the Standing Stone was not a "barrow," itself. Yet, Tolkien was very specific about the warning and how the Hobbits failed to pass the Stone on the West.

I suspect that Priya's question here does not relate to how the Standing Stone fit into the narrative, but rather focuses upon the mythological significance of the Stone. However, the inspiration for the Stone and the barrows would clearly be Stonehenge and similar ancient sites in England.