Thermal conductivity is another way to say heat transfer, and good thermal conductivity to your heatsink means lower temps for your processor. Thermal interface material is an important part of the thermal interface between your heatsink and processor. It fills the microscopic pits and valleys that can form between two pieces of metal. Since the thermal interface material has better thermal conductivity than air, more heat can flow from the heat source (processor) to the heat dissipation device.