Ductility of metals is the ability to be drawn out into fine wires - i.e. when subjected to Tensile Forces, Gold and Silver are so Ductile they can be drawn out into fine threads.
A Silversmith may draw Anealed Silver wire through progressively smaller holes in a Draw Plate until the wire is thin enough to be used in Filigree Work for example.
Copper and Aluminium are commonly drawn into wires to be used as electrical conductors. In addition, the Ductility of Aluminium makes it very suitable for Extruding sections.
Ductility is similar to Malleability but not quite the same. Lead for example, although very Malleable is not very Ducitle since it is weak in Tension