A material that lets electricity flow easily. This is because the electrons are loosely bound to the nucleus, meaning there is little to no energy required to pull the electron away. This gives conductors a non-existent bandgap, where the valence and conduction bands are literally touching or even overlapping.
A material that conducts electrical current very well.
Electronic Devices : Conventional Current Version, 9th Edition by Thomas L. Floyd
Any material that allows the free movement of electric charges, such as electrons, to provide an electric current.
Grob’s Basic Electronics, 11th Edition by Mitchel E. Schultz
In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge (electrical current) in one or more directions. Materials made of metal are common electrical conductors. Electrical current is generated by the flow of negatively charged electrons, positively charged holes, and positive or negative ions in some cases.
In order for current to flow, it is not necessary for one charged particle to travel from the machine producing the current to that consuming it. Instead, the charged particle simply needs to nudge its neighbor a finite amount who will nudge its neighbor and on and on until a particle is nudged into the consumer, thus powering the machine. Essentially what is occurring is a long chain of momentum transfer between mobile charge carriers; the Drude model of conduction describes this process more rigorously. This momentum transfer model makes metal an ideal choice for a conductor; metals, characteristically, possess a delocalized sea of electrons which gives the electrons enough mobility to collide and thus effect a momentum transfer.
As discussed above, electrons are the primary mover in metals; however, other devices such as the cationic electrolyte(s) of a battery, or the mobile protons of the proton conductor of a fuel cell rely on positive charge carriers. Insulators are non-conducting materials with few mobile charges that support only insignificant electric currents.