If something happens memorably, it is so good, so enjoyable, or so unusual that it stays in your mind. This is the adverb from memorable — it tells you how something was. A singer can perform memorably. A meal can end memorably. A mistake can be memorably bad (yes: even a disaster can be worth remembering). Though actually, people mostly use it for the good kind of “I will not forget this,” and reviewers love it: “memorably funny,” “a memorably quiet last scene.” It is a little more at home in writing than in speech; in speech someone might just say “in a way I will never forget.”