Those vases were to preserve foods and they must have been the target of rats. It's no doubt that they desperately wanted to find the way to get the rats away and I'm sure they tried whatever they could think of.
They put the pattern of snakes on the surface of the vases and sometimes also the handle in the shape of a snake. Those vases are called "vase with a snake handle."
In my opinion, snakes were one of the sacred symbols which protect human's life in Jomon culture.