When electrons travel through a conventional metal based wire they encounter resistance as they bump into atoms, defects and impurities. Carbon nanotubes can conduct electricity better than metals due to something known as ballistic transport.
Ballistic transport occurs when an electron is able to travel without being impeded by atoms, molecules, defects or impurities within the transport medium. Ideally the electron will encounter only the walls of the material which serve to impart a change of direction to the electron.
When an electron travels through a carbon nanotube, it is governed by the rules of quantum mechanics and moves as if being propelled through a smooth channel with no obstructions. This lack of resistance translates to high electrical conductivity and high efficiency as energy is not lost as heat. Wires made from carbon nanotubes could be much thinner than conventional wires, yet carry much greater currents.
Due to electrons moving through carbon nanotubes following the laws of quantum mechanics, the electrons uses a method called quantum tunnelling to move to another nanotube. This method sees the electron simply pass through the walls of the tube and appear in the adjacent tube. Much the same as if you were to walk down a corridor and simply appear in the room you wished to visit without the use of a door.