I admit, I’m to young to know what this was. I had to post it to Facebook to find out from older people that this was a spring house.
They were very important buildings on farms before electricity and other methods of refrigeration came into use. The idea was so simple; Use the cool air rising from a spring to cool a building.
Some were made of wood, but the moist air would rot them quickly. Many times wood was used temporarily until enough fieldstone could be gathered to make one out of stone.
Why this one survives when I have never seen another, I don’t know. Here is a better explanation of spring houses if you’re interested.