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.
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.
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.
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.
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).
