In thermal conduction, heat is transferred from a hot region to a cooler region through a material. At the hotter end, atoms vibrate more energetically than at the cooler end. The atoms don't flow---instead the energy flow through the material is passed along by the vibrations.
The rate at which heat is conducted along a bar of length L depends on the length, the cross-sectional area A, the temperature difference between the hot and cold ends, TH - TC, and the thermal conductivity k of the material.
There is a one-to-one correspondence between electrical and thermal conduction.
The rate of energy transfer has units of power. If an amount of heat is
transferred at a constant rate in a time t,
|≡ G (TH - TC)|
Here the thermal conductivity Κ is an intrinsic material property, while the thermal conductance G involves both material properties and geometry.
Units of Κ:   power/(length∗degrees K).
Metals generally have high thermal conductivities because they contain freely moving electrons that are efficient at transferring energy. Copper, for example, has a thermal conductivity of 400 W/(m K), compared to 0.024 W/(m K) for foam insulation.
Note: thermal resistance and thermal conductance are completely analagous to electrical resistance and electrical conductance.
Insulating materials are rated in terms of their R values, which is proportional to (but not exactly equal to) their thermal resistance. Higher R means lower conductivity. In terms of the thickness L of the material, R ≡ L/Κ.
Some typical R values (per inch):