Hierarchically tells you how something is arranged: in levels of importance, one above another. A company may be organised hierarchically. Information may be stored hierarchically, with big groups that split into smaller groups. It is the adverb that belongs with hierarchical, and it lives in the same formal world — reports, textbooks, talk about systems. You almost never need it in casual chat; people more often say 'in a hierarchy' or 'by rank.' Though actually, when writers choose hierarchically, they usually want you to see the structure, not just the idea of someone being the boss.