Salts were just small serving dishes on a low foot, made to offer some extra salt to the dinner guests. They were made as parts of the large western dinner sets that were ordered from China by the end of the 18th century. What makes them rare, is that it seems like a dinner set of several hundred pieces only had a few - maybe two or not more than four - salts to the entire set.
Since the almost only way there were to preserve food at that time, in the general mind salty food was the same as "healthy" or at least "not spoiled".
It was therefore a general suspicion against fresh food, which probably could be overcome by adding some extra salt to even the best possibly, fresh food.
At the same time salt was a necessity and very expensive, which could explain the small number as well as the fact that their well seemingly would not be big enough for holding more than a few grains of salt.