Used to find the depth of water you are fishing. A good Plummet will have a flat bottom that makes it more accurate. The hook is fed through the ring or hoop at the top, and then pushed into the soft material (usually rubber, foam, silicone, or cork). This stops the plummet from falling off and does not blunt the hook.
A Plummet is used to feel for bumps and dips, soft and hard spots, as well as helping to find the depth.
The picture shows 10g version, but a 20g Plummet is better for general purpose fishing.