A crucible does one job and is built entirely around doing it reliably: it holds a solid or molten material in direct contact with the most severe heat a furnace or torch can deliver, without breaking down itself before the material inside melts, reacts, or burns away as intended. Its walls are thick and made from a material chosen specifically to resist thermal shock and extreme temperature, historically fired clay and later graphite or ceramic, so that the crucible itself survives being plunged into intense heat and then cooled again, repeatedly, without cracking.
Because it is meant to sit directly in or over the hottest part of a fire or furnace, rather than being shielded from it the way a muffle furnace's contents are, a crucible was the tool of choice specifically for operations that needed the full, unbuffered heat a fire could give, melting metal for casting, calcining a mineral down to its ash, or holding a small weighed sample during a fire assay so its true metal content could be read from what remained. Tongs, rather than bare hands, were used to place and remove a crucible from the fire, since the vessel itself became as hot as whatever was inside it. A crucible's small size compared with a furnace or a kiln also let an operator run a test on a tiny sample before committing a whole batch of material to the same treatment.