1) Haman descends from Amalek, and by blotting out his name with noise, we are fulfilling the mitzvah of completely wiping out any remembrance of Amalek, because the gematria of מחה אמחה – “I shall surely wipe out [the remembrance of Amalek]” (Shemos 17:14), equals the gematria of זה המן – “This refers to Haman.” It is also interesting to note that Haman’s name appears in the Megillah fifty-four times, corresponding to the respective gematrias of the words מחה and אמחה, each equalling . Therefore, the blotting out of his name each of the fifty-four times symbolically wipes out his every last trace. (Mateh Moshe 5:1006; Sefer Matamim, Purim 6)
2) There is a hint in the Torah to this minhag. In the pasuk: והיה אם בן הכות הרשע – “When the guilty man incurs the penalty of lashes” (Devorim 25:2), the last letters of the word והיה אם בן spell out the name המן. When we substitute “Haman” for those words we get המן – הכות הרשע – “Haman, lash at the wicked man.” In other words, one should lash out and hit Haman, which we do by banging at each mention of his name. (Mateh Moshe 5:1006)
3) The practice of banging and making a noise at the mention of Haman’s name in the Megillah developed from an old Purim minhag of Jewish children. To fulfil the mitzvah of erasing Amalek, they would draw a caricature of Haman or write his name on pieces of wood or stone, and beat them until the images of writing wore off. Similarly, many had the minhag of stamping their feet when they heard Haman’s name, thereby fulfilling the mitzvah of stamping him out. (Avudraham, Tefillos Purim; see also Mishnah Berurah 690:17:59)
