How does conduction work?

Answer 1

In this context we will assume you are referring to thermal conductivity. Thermal conductivity is the macroscopic effect of molecules in a substance colliding with or otherwise coming close enough to other molecules in a substance to impart some of their kinetic energy (translational, vibrational or rotational) to the other molecules. Molecules close to the higher temperature surface (heat source) collide with it and pick up some of the energy of the molecules there. As they bounce away, they collide with other molecules further away and give up some of their energy to the other molecules because they have more energy than the other "cooler" molecules. This process propagates through the substance with the net effect that heat is "conducted" from the heat source to the heat sink. In conduction, each molecule stays pretty much in the same general region during the entire process, just rattling around within its home area. This differs from convection where there is a bulk movement of gas or liquid from one place to another. In the case of convection - a mass of fluid (gas or liquid) moves from an area of one temperature to an area of a different temperature, like the blobs of wax in a lava lamp. Once it gets to a new area, it imparts its energy to (or absorbs energy from) the new surrounding fluid by way of conduction.

Answer 2

It's the transfer of heat.