A that time in history storage of food (and also extra grain, extra firewood and so on) was often in a souterrain. A souterrain is a sort of cave-cellar but with a long entrance tunnel because they were also used as a refuge for the family if the homestead was attacked. The long tunnel made it easier to defend.
Sometimes the souterrain had an entrance in one of the houses but often they were completely separate buildings with a small entrance somewhere in the compound.
I think the rectangular stone building in the background of that image is a barn so we have two storage building types that could be made, the barn and the souterrain.