Makes Soup So Good?

I think it is because every culture in history has had a "lower" class that has had to make do with the cheapest, least sought after ingredients. Higher "quality" ingredients often have as much to do with texture as with flavor, and the richest people in any society get the pick of the tenderest cuts of meat, the finest spring vegetables, and the freshest fruit. In contrast, the "peasantry" lives on the tougher cuts of meat, the bones often included, root vegetables and leftover fruit that has either been dried or fermented.
Bones, gristle and similar tissues contain, among other things, collagen. This is a protein used in connective tissues, and it has some very interesting properties. Firstly, it dissolves in hot liquid. Second, it coagulates when it cools down, provided it is concentrated enough. If this makes it sound like gelatin, then you are correct: collagen is one of the main ingredients in gelatin. The third property of collagen that is of interest in the kitchen is that is carries flavors that water cannot.