Sinkers add casting weight and hold a bait where you put it. On still water that is mostly about distance; in a river it is about staying put, and you want the lightest weight that still holds bottom, because anything heavier drags and looks unnatural.
The materials differ in more than weight. Stone and lead-free options are quieter on the bottom and less likely to spook fish in clear shallow water, while iron and zinc give you the same weight in a smaller shape, which casts further and holds better in a flow.
Pair a sinker with a float and you have a set depth; use one alone and you are fishing hard on the bottom, which suits species that feed there and wastes your time on those that do not.