Costumes On Purim

Question

Why is there a Minhag to dress up in costumes on Purim?

Answer 1

One "popular" reason is that the entire נס of Purim was hidden and seemed very natural (i.e. no Hashgacha to it / Hashem's name not mentioned in the מגילה). We too hide ourselves to symbolize this.

Answer 2

One of the reasons mentioned why we disguise ourselves on Purim, is to highlight the concept that even the non Jews disguised themselves, pretending to be Jews. The Megila says:

"And many of the people of the land professed themselves to be Jewish, for the fear of the Jews had fallen upon them." (8:17)

They pretended to convert to Judaism, but didn't actually. We know this because the term used in that verse is "misyahadim," -- "Judaized," instead of "misgayarim," -- "converted." Since they masqueraded as Jews, thus the custom has arisen to masquerade ourselves on Purim, to commemorate this miracle, whereby a complete turnabout caused the Gentiles to fear us and not kill us, as they had originally planned.

Answer 3

The benei Isaschar says (Adar, Maamar 9:1) that as the jewish people bowed to Nevuchadnetsar externally Hashem also acted externally by making it seem as if there was a decree to destroy them. Hence, it is a custom to dress up on Purim to externally appear like non-jews.