Conduction

Conduction is the main mode of heat transfer in solids.
It is the process by which heat is transmitted through a medium from one particle to another.

In conduction, heat is transferred from one atom to another by the vibration of atoms. Heat is also transferred by the movement of free electrons from the hot end to the cool end (which is why metals are good conductors of heat.) Poor conductors of heat are liquids and gases.

Conduction occurs in direct contact
e.g. solid to solid (shaking of hands), solid to liquid (diving into the water)

How Conduction Works
When one end of a rod is heated, the particles at this end of the rod gain energy and start vibrating faster, which will then cause the particles to collide with the other particles. Some of their energy is transferred to the other particles which will let the other particles gain kinetic energy. In this way, heat is passed along by the vibrating particles.