Conduction of Heat is a process where heat is transferred from the hotter part of the body to the colder part without involving any actual movement of the body molecules.
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 continue as long as heat is still being added
The transfer between bodies continue unit the temperature different decays and a state knows as thermal equilibrium occurs. Greater the value thermal conductivity K of body better is its heat conducting capability.
For insulator this value of K is zero.