Thermal mass is the ability of a material to absorb and store heat energy. In building design, thermal mass are properties of a building's assemblage which provides "inertia" against temperature fluctuations. Appropriate use of thermal mass throughout a building can make a big difference to the comfort, heating, and cooling costs of a project.
The benefit of thermal mass is shown in comparison of how heavy and light weight constructions affect internal temperatures. For example, when outside temperatures are fluctuating throughout the day, a large thermal mass within the insulated portion of a building's wall assembly can serve as a mitigating barrier to "flatten out" the exterior temperature fluctuations, absorbing a lot of heat without warming up very much. Since the building's heavy weight construction will absorb the thermal energy when temperatures are higher, it will give thermal energy back when the surroundings are cooler without reaching thermal equilibrium. For lightweight construction, low thermal mass materials only absorb small amounts of heat before quickly releasing them and reaching their equilibrium. For example, when temperatures are constant a material with a low thermal mass like timber, will absorb and quickly release the thermal energy into the air. If you have a timber floor with exposure to direct sunlight during the low temperature periods, it will heat up the room more so that a material with a high thermal mass.
This is distinct from a material's insulation value, which reduces a building's thermal conductivity, allowing it to be heated or cooled relatively separate from the outside, or even just retain the occupants' thermal energy longer. Remember that your first priority should always be your insulation, including the use of windows and frames with a high R values. If your home is poorly insulated, thermal mass can even make your house less comfortable and increase your energy use.