Conduction in metals and non-metals

In metals, conduction happens due to the combination of vibrations of molecules and free electron diffusion. While in non metals, the mechanism for conduction is only atomic or molecular vibrations.

What is atomic or molecular vibrations?
When thermal energy is supplied to one end of the rod, the particles (atoms or molecules) at the hot end vibrate vigorously. These particles will collide with neighbouring particles, making them vibrate as well. Thus, the kinetic energy of the vibrating particles at the hot end is transferred to the neighbouring particles.
This process is slow.

What is free electron diffusion?
When the coppper rod is heated, the free electrons in the copper gain kinetic energy and move faster as a result. These fast-moving electrons then diffuse or spread into the cooler parts of the metal. In the process, they collide with the atoms in the cooler parts of the metal and transfer their kinetic energies to them.
This is a much faster mechanism of thermal energy transfer.

This explains why the conduction in metals is faster than in non-metals. Thus metal is a good conductor of heat and non-metals is a poor conductor of heat.

metals, eg. copper, silver, steel and iron

non-metals, eg. glass, plastic, wood, brick, wool