In conduction, the heat transfer takes place at the molecular level without actual movement of molecules, from the hottest to the coldest surface.
In the process of heat transfer, the molecules pump into their neighbors and transfer the energy to them which continues as long as heat is still being added.
The transfer between bodies continues until the temperature difference decays and a state known as thermal equilibrium occurs.
Greater the value of thermal conductivity K of a body better is its heat conducting capability.