This is the adverb for that same study of ancient societies — buildings, graves, tools and the rest. You use it when you mean “in the way archaeology works” or “from that study’s point of view.” A place can be archaeologically important even if it looks empty today; a broken pot can be archaeologically richer than a gold ring, because it tells you more about ordinary life. Though actually, it is a long, stiff word: in speech people often just say “for archaeologists” or “in archaeology.” It does not mean “a very long time ago” on its own.