It's generally a translation error or just some marketroid using a term they don't understand but have heard of.
Generally, these are devices which do not have any aluminum electrolytics, but rather only "solid tantalum" type electrolytic caps (and usually a bunch of ceramics, too). Note that I've seen this label on boards which decidedly have aluminums, too, but in those crappy surface mount packages. People who make up that marketing fluff really usually have no clue what they are talking about.
Now, tantalum electrolytics do tend to be more reliable than the aluminum type, so if they really do mean that there are no aluminums, that can be a good thing from a reliability point of view. That isn't to say that tantalums can't fail or are all of high quality, but they do tend to behave a bit better than the aluminum types.