La Cucaracha ("The Cockroach") is a traditional Mexican corrido (folk ballad), ubiquitous at celebrations like Cinco de Mayo. While the song has many verses, the cockroach character is a popular humorous costume.
Since the song is often sung in everyday clothes, a nice shirt/blouse and pants/skirt is perfectly acceptable for a party. The character costume is for fun/theatrical effect.
The song's lyrics vary—some historical (referencing Pancho Villa, marijuana), some playful. The cockroach is a resilient, adaptable symbol—much like the Mexican spirit.