What is the Units for Thermal conductivity? What are the units for thermal conductivity and why?
 A: Thermal conductivity is, as Mark writes, is in SI units measured in $Wm^{-1}K^{-1}$, i.e. $\frac{power}{distance \times temperature}$
However, the $m^{-1}$ needs a little more explanation.
The rate of heat flow is proportional to the surface area, and inversely proportional to the thickness. So for the unit of thermal conductivity, thickness gives a $distance^1$ in the numerator, and surface area gives a $distance^2$ in the denominator.
Hence, thermal conductivity is $\frac{power \times distance}{distance^2 \times temperature}$.
And so when we cancel $distance^1$ from numerator and denominator, we get $\frac{power}{distance \times temperature}$
A: Thermal conductivity has dimensions of $\mathrm{Power / (length * temperature)}$. Power is the rate of heat flow, (i.e.) energy flow in a given time.  Length represents the thickness of the material the heat is flowing through, and temperature is the difference in temperature through which the heat is flowing.
In SI units, it is commonly expressed as $\mathrm{Watts / (meter * Kelvin)}$, and in US units, it is commonly given in $\mathrm{BTU/hr/(feet\ *\ ^oF)}$.
It expresses the rate at which heat is conducted through a unit thickness of a particular medium.  That rate will vary linearly based on the temperature difference across the material, so it is expressed as a value per degree of temperature difference, thus Heat Rate per unit thickness per degree of temperature difference.
A: You might need to look up R-Value which is closely related to thermal conductivity and is being used in so many case instead.
The units are 
$
\frac{(ft^2.h.^{\circ}F)}{BTU}
$
in US and 
$
\frac{(K.m^2)}{W}
$
in SI.
These two units (Thermal conductivity and R-Value) can be converted to each-other very easily doing Say if x is our Thermal conductivity value for our material, hence R-Value will be,
a is the thickness in Meters
$$
\frac{1}{x}* (a)
$$
