Astonishingly means “in a way that is very hard to believe,” or “to a surprising degree.” Writers like it at the front of a sentence, where it comments on the whole fact: “Astonishingly, nobody was hurt.” It can also sit in front of an adjective: astonishingly good, astonishingly cheap — so good or cheap that you almost cannot believe it. That is the same job as amazingly or incredibly, only a little more formal. In speech, people often prefer those casual twins, or just “I can’t believe…” The word does not change the facts; it tells you how surprising the speaker finds them.