Conduction: The transfer of energy form the more energetic particles of a substance to the adjacent less energetic one as a result of interactions between the particles. (solid, liquid, gas)
In liquids & gases, conduction is due to the collision & diffusion of the molecules during their random motion.
In solid, it is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons.
The rate of heat conduction through the medium depends on the geometry of the medium, its thickness, and the material of the medium, as well as the temperature difference across the medium.