thermal conductivity
Grab a metal pan handle straight off the stove and you yelp; grab a wooden spoon that has sat in the same pot and it is comfortable. Both touched the heat, but the metal rushed it into your hand while the wood held it back. Thermal conductivity measures exactly this: how readily a material lets heat flow from its hot side to its cold side.
Heat is just vigorous atomic jiggling, and conduction is that jiggling being passed along from atom to atom toward the cooler regions. In a non-metal the heat is carried by phonons — packets of lattice vibration ferrying energy across the solid. In a metal, the free electrons can also carry heat, and they do it so well that metals far outpace everything else. The faster and farther these carriers travel before being knocked off course, the higher the conductivity.
Thermal conductivity matters for cookware, insulation, computer chips that must dump their heat, and spacecraft that must keep it in. The subtlety is that the very best heat conductors are not always metals: diamond, an electrical insulator, conducts heat better than copper, because its light, stiffly bonded atoms let phonons sail across it almost unhindered.
Touch a tile floor and a carpet in the same cool room: the tile feels far colder. Both are at the same temperature; the tile only feels colder because its high thermal conductivity whisks heat out of your foot quickly, while the carpet conducts so poorly that the heat stays put.
Tile feels colder than carpet at the same temperature — that is thermal conductivity, not temperature.
In most metals heat and electricity ride together, so good electrical conductors are usually good heat conductors. Diamond is the famous exception: it blocks current completely yet conducts heat superbly through phonons alone.