I understand the following properties:
Thermal Conductivity: It tells how well thermal energy can get transferred to a material, from a material and within the material. A material with higher thermal conductivity will allow more energy transfer to it, within it, and from it.
Specific heat: The amount of energy required to raise/drop the temperature of a unit mass by one degree Celsius. Higher the specific heat difficult it will be to increase the temperature of a material.
Thermal diffusivity clubs these two properties.
Consider water and air. Air has a higher thermal diffusivity than water? What does this physically mean.