Zeolites are very similar to clays, with one key difference. The molecular structure of clays is rather compact. In contrast, the molecular structure of zeolites has tiny molecular-sized holes, and these holes are wont to connect. The result is a porous, tunnel-filled structure at the molecular level.
The resulting tunnels make zeolites very good at absorbing substances that fit very nicely in those tunnels. What those substances are depends on the zeolite. There are a large number of naturally occurring zeolites, and even larger number of manufactured zeolites. Which zeolite absorbs what substance depends very much on the nature of the holes in the zeolite. As an example, the International Space Station uses a particular kind of zeolites ("zeolite 5A") to selectively absorb carbon dioxide from the breathing atmosphere.
Zeolites would need to be discarded after becoming saturated if all they did was absorb stuff. That's not the case. It's rather easy to make zeolites relinquish the stuff they have absorbed because the absorption mechanism is rather weak. All it takes is a smallish amount of energy. Zeolites used in industrial settings are subjected to heat, noxious chemicals,or both to make them relinquish the stuff they have absorbed.
In addition to having a large number of industrial uses, zeolites have apparently become attractive to the "all natural" crowd. (I suspect the larger number of "non-natural" zeolites are verboten amongst this crowd.) Exposing zeolites to sunlight means they absorb heat and ultraviolet light. This is indeed one way to make zeolites reject whatever has been absorbed. That's not very efficient; it would be much more efficient to bake those zeolites and/or expose them to a series of caustic chemical baths. However, that wouldn't play well with the "all natural" crowd.