Explain the process of heat transfer, as conduction is part of that overall process. Heat transfer occurs when the temperature of an object is changed because of the temperature of another object. The temperature can be raised or lowered because of the addition of the object to the environment.
Talk about the process of conduction specifically. Heat conduction occurs when the temperature changes because one object is in direct contact with another object. Ask the person you are explaining the concept to if he has any questions before moving on.
Show the person examples of heat conduction. For example, when a pot of water is on a stove top heat is being conducted from the stove top to the pan to the water. Another example is when a person touches ice and the temperature of the ice affects the temperature of the person's hand.
Explain that scientifically, heat conduction occurs because the molecules in an object are being agitated or slowed down. When they are next to an object with molecules of a different speed, it is natural for the molecules to want to create a balance. Therefore the faster moving molecules move into the area where the slower molecules are until eventually the two objects' molecules are equal.