This is the
birthdate of
Asuka Langley Sohryu in
Neon Genesis Evangelion. It is actually a reference to
Asuka's
Japanese Seiyuu (
Voice Actor)
Miyamura Yuuko's birthdate. Miyamura was born on
December 4, 1972 in
Hyougo. Both Asuka and her
Seiyuu share the same
blood type,
O, as well.
Among Eva no otaku there is a subset of Asuka Otaku who vehemently deny there is an Asuka vs. Rei debate at all and would say Anta baka?! to anyone who says otherwise. Come this date, fans of Asuka's breasts from around the world will unite to celebrate the coming of whom they consider, the chosen one. Rei Ayanami won't be "created" for another three years at least so among the Evangelion fan community this date signifies "proof" that Asuka is better than Rei.
It is also a perfect example of how much symbolism and how many references are piled into Eva. All of the main characters in Evangelion share the same birthdays as their seiyuu. Most also share the same blood type. It is this sort of connection; the effort to make the characters "real" that I think really sets Eva apart from other anime.