Electricity depends upon the flow of electrons. Whenever electrons can flow easily through a structure, then that structure is said to be a good electrical conductor. Clearly, the very fluid nature of the electron sea allows it to be a very good electrical conductor. Because of this quality, metals are usually used in the electronics industry. Metals are also known as being good conductors of heat, or thermal conductors.
Heat is kinetic energy.
In order for a substance to conduct heat, it must be able to transmit kinetic energy. If heat is applied to one side of a piece of metal, then the kernels will start to vibrate. Because they are so loosely held into the crystal structure, they will be able to vibrate freely. With the increase in the amount of their vibration, they will run into the kernels located next to them. That will start more kernels to vibrate.