Something that’s ductile is “easily molded or shaped”, “easily drawn into wire or hammered thin”, or “easily influenced”.
It’s actually related to the word duke, because both words come from the Latin word ducere “to lead”. Ductile came about through the Latin word ductilis, meaning “that may be led or drawn” (OED). Still, I think the connection is a bit of a stretch. But I guess if you can be led by someone, you might be also be easily influenced.
Despite its broad definitions, I’ve found that ductile is almost always used to describe metal. Scientifically speaking, ductility is “a mechanical property which describes how much plastic deformation a material can sustain before fracture occurs”. I thought that maybe duct tape was somehow related to this, but nobody else thinks so!