 Electrical conductivity is a measure of a material's ability to conduct an electric current.  Metals are considered to be good conductors of electricity.  Conductor implies to the material that the outer electrons of the atoms are loosely bond with and free to move through it.  When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current.  Resistivity is the measure of strongly an atom opposes the flow of electricity (Its the power to resist electricity). Electrical conductivity is affected by resistivity. Hence, Electrical Conductivity is inversely proportional to resistivity. Insulators have high resistivity.  Resistivity depends upon 2 factors : 1. The length of the wire: The longer the wire the higher the resistivity. 2. The cross-sectional area of the wire: The larger the cross-sectional area the lower the resistivity.

 Thermal conductivity is the property of the material that indicates is ability to conduct heat.  The thermal conductivity of this metal is, like electrical conductivity, determined largely by the free electrons. Suppose now that the metal has different temperatures at its ends. The electrons are moving slightly faster at the hot end and slower at the cool end.  The faster electrons transmit energy to the cooler, slower ones by colliding with them, and just as for electrical conductivity, the longer the mean free path, the faster the energy can be transmitted, i.e., the greater the thermal conductivity.  Video:

 In metals, there are free held loose electrons because they form metallic bonds with each other which creates a sea of electrons.  Metals have low resistance and high electrical conductivity.  Most atoms hold on to their electrons tightly. But most metals don’t.  For instance, in a copper wire when an external influence of electrons is passed, the electrons present in copper find it repulsive so they move away from each other.  This forms a chain of such events and it is called an electric current. It propagates through the material at the speed of light.  Although graphite is a form of carbon (a non-metal), it also conducts electricity because of the arrangement of its atoms.

 Metals are particularly good conductors of heat because their particles are very closely packed so the vibrations are passed on very quickly. They also contain large numbers of "free electrons".  These drift slowly through the structure, giving metals their strength and other properties.  As the metal is heated, the free electrons closest to the heat source are heated.  This makes them move faster and they travel through the metal, colliding with both atoms and other electrons.  This naturally makes these vibrate faster (or move through the metal faster - in the case of collisions with other free electrons). Thus the heat is passed quickly through the metal.

 An element, an alloy, or compound that will conduct electricity without resistance below a certain temperature are superconductors.  They show zero resistance at specific temperatures.  A superconductor of niobium and titanium has huge applications, it becomes superconductor at 9.5k.