Thermal Mass is not an "it" but rather a property, like weight. Every object absorbs, retains and releases stored heat, but some hold more than others. An object that holds a lot of heat energy is said to have, or be, a Thermal Mass.
The simplest way to think of a Thermal Mass is to visualize a dump truck next to a compact car on a flat, smooth parking lot.
The truck takes more energy to get moving, and keeps rolling further after one stops pushing. It has more mass.
The compact car gets moving easily, but won't keep rolling as long.
It's not a perfect picture, but it suffices to get the idea across. Let's take a look at it in woodstove terms:
A metal woodstove is a light stove. Light a fire and it will put out heat very quickly, but let the fire go out and the heat stops just as quickly. The knack for getting a metal stove to heat a home well is to smoulder the wood just hot enough to keep a little heat coming out. This is simply bad combustion. Wood burns better when it can burn hot, but that's a digression.
Let's add some Thermal Mass to the wood stove, say, soapstone. Take a 200 pound metal stove, add 300 pounds of soapstone and you've got a night and day difference. The now 500 pound stove holds heat much longer, keeps the fire going better, and makes the space heated much more comfortable with less re-loading effort.
Let's add more thermal mass and consider an oven or a masonry stove.
3,000 - 5,000 pounds is a typical weight for a masonry heater, though some weigh up to 10,000 pounds. Now we're talking about heat storage. A thermal mass of 10,000 lbs of masonry will hold heat for days!
For ovens and masonry heaters thermal mass = thermal stability. Ovens cook the food after the fire goes out, and heaters heat the house after the fire goes out.
The challenge of good design is to match the thermal mass to the heat output needed. To small an oven and you won't..... (I don't know beans about ovens)
If a heater is too massive you will find yourself living with an unresponsive behemoth. Balancing mass to heat output needed is something that must be considered during the design process. A custom heater builder can match your heater's performance to your desired lifestyle, so that the truck rolls just as far as you need it to for each push you want to give it.