When you use water as a heat storage medium, you are storing the heat in the kinetic energy of the water molecules. In common parlance, you are increasing the temperature of the water. Obviously, over time the water's temperature will gradually revert to the ambient temperature, and you will lose all the heat you stored in it.

In contrast, when you store heat in Zeolite, you are not storing it as kinetic energy, you are driving an endothermic chemical reaction that stores the energy in high-energy chemical bonds. After you are done heating the Zeolite to "charge" it, it will return to the ambient temperature, but it still has (lots of) energy stored in the chemical bonds. This energy does not dissipate in the way that the kinetic energy of a high-temperature substance would. The energy can only be released by reversing the chemical reaction, so it is securely stored. You can then transport the Zeolite at ambient temperature to a location in need of heat, and then add water, which reverses the chemical reaction and releases the heat again.

So it doesn't actually store "heat", it takes in heat (i.e. molecular kinetic) energy and stores it in a different form (chemical bond energy).

So then it could be used to store heat created from a reactor then transported where the heat is needed?

Yes, that is the general idea.

You would always lose heat as black body radiation for the period of time the Zeolite is hotter than the environment!

I assume it means that, because it is stored in the chemical structure rather than actual heat, it's not leaking to the environment while the pellet is sitting on a shelf (if not exposed to the elements).

What they mean is that when the Zeolite is "heated", then it can be stored indefinitely without "cooling down". If you heat water and put it in a tank, it will lose its heat relatively quickly. The Zeolite stores the energy from heat in (stable) chemical bonds, so it won't lose energy over time.

Can you give me some examples of how this can be used?

You can heat Zeolite using solar power during the day and release the energy at night. Current thermal energy storage techniques use stuff like molten salt (http://en.wikipedia.org/wiki/Thermal_energy_storage), which is a lot harder to work with than pellets.

Yeah, but once you do that, how do you get the water back out? It sounds like this stuff doesn't do that very easily.

From what I understood, the water comes out when you heat it.

The article gives one example: you could charge them with waste heat at plants and factories, then transport them to homes and offices where (I suppose) they could be used for heating and hot water, at some later point in time.

Sounds more efficient than teleheating via insulated pipes: http://en.wikipedia.org/wiki/District_heating

This is a great application. It could be particularly useful in the New England states. Manufacturing could store their waste heat in the zeolite, and resell it to homes and businesses who can use it to heat up during the winter. It could be a major disruption to utility companies.

Considering the transport cost and equipment needed, I'm not convinced that would be economically viable...

Water heater in your home. Deliver heat when needed by pouring water on stones, comes out hot. Doesn't have to keep water hot and ready; so probably save 90% of the energy currently leaked away due to Newton cooling (hot water heater cooling off all day while you're at work).

Think of it as a rechargeable heat battery.