Thermal conduction is the direct sharing of kinetic energy (heat) between materials in contact, specifically when talking about heat transfer. This is because higher internal energy of an object means that its molecules are moving faster. Conduction is the main mode of heat transfer between solid materials. It is in large part responsible for energy losses from buildings, and it is also how gas and electric stoves heat up pans.
A region with greater thermal energy (heat) corresponds with greater molecular agitation. Thus when a hot object touches a cooler surface, the highly agitated molecules from the hot object bump the calm molecules of the cooler surface, transferring the kinetic energy and causing it to heat up. This is illustrated in the figure below:
Conduction is the main mode of heat transfer for solid materials because the strong inter-molecular forces allow the vibrations of particles to be easily transmitted, in comparison to liquids and gases. Liquids have weaker inter-molecular forces and more voids between the particles, which makes the vibrations of particles harder to transmit. Gases have even more voids, and therefore infrequent particle collisions. This makes liquids and gases poor conductors of heat.