Thermal conduction by atomic collisions
Conduction is the transfer of thermal energy through a material from one particle to another.
If you hold a piece of ice in your hand, it will begin to melt. This is because thermal energy is transferred from your hand to the ice by conduction.
Particles in solids that are in hotter regions vibrate faster. These particles collide with their neighbours and transfer some of their energy. These particles then also begin to vibrate faster.
In this way energy is transferred across the material.
Solids conduct heat better than liquids or gases. The particles inside solids are packed more closely together so the particles collide more often. This leads to a faster transfer of energy.