Quick answer
The conductor is the metal core of a cable — the part that actually carries the electric current. Everything else in the cable (insulation, sheath, any armour) exists to protect the conductor and keep the current safely contained.
Conductors are made from either copper or aluminium: copper for its high conductivity and durability in most internal wiring, aluminium for its light weight and lower cost in larger feeders and overhead lines. A conductor can be a single solid rod or many stranded wires, the latter giving flexibility.
A conductor's cross-sectional area, measured in square millimetres (sq mm), determines how much current it can carry — its ampacity. APAR uses high-purity conductors in its house wires and cables.