thermal conductivity is a proportionality constant in Fourier's law, a flux equation which states that conductive heat flow through a homgeneous solid medium is proportional to the cross-sectional area perpendicular to heat flow and to the temperature gradient.
http://www.taftan.com/thermodynamics/FOURIER.H TM
Thermal resistance is the inverse of the thermal conductivity.
The higher the thermal conductivity, ther easier it is for conductive heat transport. However, as thermal resistance increases, it is more difficult for heat to travel throught the solid medium.