The distinct difference between Purim and the other great salvation's that we experienced is that the salvation of Purim was totally hidden. Unlike the splitting of the sea which totally broke the rules of nature, the "Purim Miracle" did not. One could read Megillas Esther, and view all the pieces that Hashem wove together to bring about the downfall of Haman and the rise of Mordechai as pure coincidence. But we all understand that this was Hashem's direction which orchestrated all of these amazing events which would lead to our salvation. When we understand from the Purim story that it is G-D who is running everything, even the things that seem like they are "just natural", this leads to happiness. We then realize that our entire lives are being directed in a very specific way by the One Above, every seemingly mundane thing that "occurs" or "happens" to us is in fact all part of G-D's plan and doing. This understand should fill a person with great happiness and this is highlighted through the Purim Miracle. It was this realization that Haman and his ancestors attempted negate. They wanted everyone to think that the world was just a set of natural occurrences with no real Master or Plan. As we read this Shabbos the story of Amalek's brazen attack on the Jewish People, we can strengthen ourselves in the realization that nothing happens by chance and everything is in G-d's Plan. In this way we can wipe out the memory of Amalek on a spiritual level.