Conductors are materials that allow electrons to flow relatively freely. They are generally metals, materials in which some electrons are able to move with a relatively low binding force to surrounding positively-charged nuclei. Hence conductors are widely used in electrical components, including wires to allow the flow of charge, parallel plates to allow storage of charge, etc.
Insulators are materials that possess more rigidly bound electrons. Hence electron flow is essentially zero through an insulator. A common use of insulators in electrical components is the encasing of more conductive materials in order to prevent electrical discharge. Examples include the insulating plastic and ceramic around conductive wires, conductors, inductors, etc.