Answer:
It reduces energy transfer by preventing two different types heat loss:
- Radiant heat loss: The lid prevents the kinetic energy (heat) of the liquid from being passed to the molecules in the air.
- Conductive heat loss: The sides and bottom of the mug are insulated. This is done in two ways; either there is a pocket of air (sometimes even a vacuum) between the inside layer and the outside layer of the mug, or there is a foam/sponge like insulation between these layers. Both methods work on the same principle. Because the layer of air/insulation is *less dense* than just the single wall of a normal mug, the molecules are *farther apart*, so it is "harder" for the heat to be transfered.
Think about a cake that has just been pulled out of the oven. You can touch the cake for a brief second without being burned, but you have to use oven mitts to touch the pan, or you will be burned instantly. This is because the cake less dense than the pan, and therefore doesn't transfer the heat to the same degree.