An unbirthday is every day in the year that's not your birthday. Either that or the day where unbirths in the BBS-era first started appearing.
It's something some dude created in a story he made up to impress his girlfriend... who was ten years old. Gotta love Cracked sometimes.
http://www.cracked.com/article_17221_6-writers-who-accidentally-crapped-out-masterpieces.html I didn't know the Information prior to this morning. I was bored and just read random articles. Happy accident I guess.