First, imagine a block of material.  It is made of many tiny particles (called atoms) that are locked in place.  They do move and shake in their place a little bit, according to their temperature.  The higher the temp, the more motion.

Imagine a heat source on one side of it...  the heat source could be a flame, it could be an infrared light, friction with a surface, or any number of other things... As the particles nearest the heat source gain energy, they move more.  These warmer particles bump into the particles nearby, transmitting their energy of motion (heat energy). A COMMON MISCONCEPTION some people believe is that the particles migrate around in hot solids.  While some particle motion is possible, the particles are "locked" in place and not free to move around... they are only able to shake more vigorously when hot.  If the particles could move around more freely, then we'd be talking about a liquid.

This energy is transmitted, particle to particle, further into the material.  Eventually, the heat energy will get all the way through.  A soup spoon that's been sitting in hot soup will eventually get warm all the way up the handle.  The faster a material transfers heat energy through itself, the higher its THERMAL CONDUCTIVITY is.

Any matter can conduct heat energy.  Air, water, rock....  anything made of atoms. Some materials let this happen rather easily.  They are called conductors of heat.  Some things do not let this happen easily; they are called insulators.  When measuring and comparing how well different materials conduct heat energy, people use that material's thermal condictivity.

Different materials are easier to heat than others.  Water is pretty hard to heat, while aluminum is much easier to heat.  A rating of this ability is called the material's specific heat.

DEFINITION of SPECIFIC HEAT:    A material property that indicates the amount of energy a body stores for each degree increase in temperature, on a per unit mass basis. Its units are Joules/kilogram-Kelvin.
 

DEFINITION of THERMAL CONDUCTIVITY:    A material property that describes the rate at which heat flows within a body for a given temperature difference. Its units are Watts/meter-kelvin

SOME PEOPLE think that these two terms mean the same thing, so I asked a friend to do a little reseach for me, and she sent me this information:
 

	Silver	Copper	Aluminum	Glass
Specific Heat	236	386	900	840
Conductivity	428	401	235	1