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