Heat conduction takes place between two objects in contact with each other. Heat energy moves from one material to the other. In heat conduction, the heat energy travels from the hot point to a cold point. Eventually, the two materials will even out in temperature as the heat keeps on transferring until the temperatures are the same. This is equilibrium. For example, a pan of hot soup is taken off the oven and put on a table. The area of the table under the pot gets hot. Heat from the pot moved to the table top by conduction.
Electrical conduction is usually done through wires or cables. Something that electrons can easily move through is a good electrical conductor. Metals are mostly good conductors. An insulator like rubber is a poor conductor. Plastics are insulators. Some materials, such as glass, are conductors for heat but not electricity.