Objects having differing temperatures try to come into equilibrium, by moving energy from the warmer to to cooler one. There are several different ways to transport the energy:
Conduction of thermal energy takes place within matter (which can be in solid, liquid, or gaseous form). The energy moves through the material without the material itself moving noticeably. We should distinguish three ranges of thermal conductivity:
Thermal conduction of energy from one object to another requires that they be in contact.
Metals are cool to the touch because they are good conductors of thermal energy. Our body temperature is fixed, and usually well above that of our environment and the objects in the environment. When we touch a object that is cooler than we are, it quickly conducts energy away, leaving our hand feeling cool. Stone and glass are better thermal conductors than air, and so they feel cold, too. This works the other way when we encounter a sun-warmed seat belt buckle -- now energy flows from the metal, again because it is a good conductor, to us, and if it's really hot, we get burned.
The opposite of a thermal conductor is a thermal insulator. An insulator is a very poor conductor. Because we are warm-blooded (and like to stay warm), insulators are important. When we touch a cool piece of foam insulation, it does not take energy away from us because it is not a good conductor. It may be very cold, but it does not feel very cool because it does not remove energy from us quickly.
Thermal conduction requires the presence of matter, and so the very best insulator is vacuum. Sometimes this is used -- a thermos bottle is a double bottle with vacuum between them.
Air and other gases are good insulators, because their density is low (so there isn't much material present to transport the energy). Most of the materials we use for insulation are really just air held in place: fur, hair, feathers, styrofoam, double-pane glass and storm windows, and woven cloth are all examples of this idea.
As you step out bed in the morning, what would you like your warm feet to meet? A good conductor, like a tile floor, or a poor conductor, like a rug? The difference is in how rapidly they will carry away energy.
Check the box when you are done:
Discussion of thermal conduction