As I read this story, the significance of the stones stood out to me more than past times when I had read it. I was amazed at the effort it would take to carry 16 large stones up a mountain, having faith that the Lord would perform the miracle you hoped for.
Symbolically we each have stones we need to carry up mountains to the Lord. In this same book of scripture we are told by the Lord: "if men come unto me I will show unto them their weakness. I give unto men weakness that they may be humble; and my grace is sufficent for all men that humble themselves efore me; for if they humble themselves before me, and have faith in me, then will I make weak things become strong unto them." (Ether 12:27)
When we bring those heavy, ugly stones up unto the Lord he can cause our weaknesses to be strengths, lighting our way. Our weaknesses can be made strong, and we can use those strengths to lead and help others.
"And thus the Lord caused stones to shine in the darkness, to give light unto men" (Ether 6:3)