Thermal conductivity is the ability of a material to conduct heat. Metals are good at heat conduction, and so are gasses. The thermal conductivity of a material is a defining property that aids in the development of effective heating/cooling technologies. A value for thermal conductivity can be determined by measuring the rate at which heat can pass through a material.
Thermal resistivity is the opposite of thermal conductivity. This means not conducting heat much. Materials with high resistivity are called "thermal insulators" and are used in clothing, thermoses, home insulation, and cars to keep people warm or in refrigerators, freezers, and thermoses to keep things cold.
Thermal conductivity is often represented by the Greek letter "kappa", . The units of thermal conductivity are watts per meter-kelvin. Watts are a measure of power, meters are a measure of length, and kelvins are a measure of temperature. From the units, we can see that thermal conductivity is a measure of how much power moves through a distance due to a temperature difference.
Silver is one of the most thermally conductive materials (and is relatively common), and because of this there are some cool experiments you can do with silver that show extremely well how thermal conduction works.
One example is when you put 2 spoons in boiling water, one spoon is steel and the other is silver. When you take the spoons out of the boiling water, the silver spoon is hotter than the steel spoon. The reason for this is that silver conducts heat better than steel. The silver spoon will also cool off faster because of this, as it is better at releasing heat.
Another example of silver's thermally conductivity is to put different materials on ice cubes. An iron washer will just sit on the ice and slowly become colder. A copper penny will melt through the ice cube and become colder faster. A silver coin, spoon, or ring on the ice cube will sink into it almost as though the ice cube were made of thick syrup, and the silver will become ice cold almost instantly. Again, this is because the silver is really good at drawing heat from the air and giving it to the ice cube. Copper is also good at this, but not as much as silver.