This type of heat propagation consists of the transfer of thermal energy between the particles that make up the system. For example: you place one end of a metal bar in the flame of a fire. After a few moments, you notice that the other end also heats up, even though it is outside the fire flame.
This happens because the particles that make up the material received energy and, therefore, began to agitate with greater intensity. This agitation transfers from particle to particle and propagates throughout the bar until it reaches the other end.
Thermal conduction occurs more or less easily depending on the atomic constitution of the material, which makes it a conductor or insulator of heat. In conductive substances this transfer process happens faster, as in metals, for example. In insulating substances, such as rubber and wool, this process is very slow.