The sheath is the outermost protective covering of a cable. It wraps and protects the insulated conductors inside, shielding them from moisture, abrasion, chemicals and general mechanical wear.
It is worth distinguishing the sheath from the insulation. The insulation sits directly on each conductor and provides the electrical barrier; the sheath is the overall outer jacket that holds everything together and protects it from the environment. In a multi-core cable the sheath is what binds the cores into one cable.
Sheath materials are chosen for the environment — typically PVC or low-smoke compounds, with tougher or armoured constructions where extra protection is needed. For fire-sensitive locations, low-smoke, low-halogen sheathing limits smoke and toxic gas, as explained under LSZH cable.