Today, Feburary 11th, is is 建国記念日, pronounced kenkoku kinenbi, and often translated as National Foundation Day. Given that I had to remind my girlfriend of this holiday (as opposed to the other way around), I questioned how popular this holiday actually was in Japan. From the basic research I've done, it seems to celebrate the crowning of the Japan's first Emperor, Emperor Jinmu, according to Shinto mythology, on February 1111th 660 BC (I have no idea which calendar-altering-events these figures take into account if any). Obviously, during 660BC, they didn't call that day "February 11", but rather this date was calculated from ancient Japanese text (the Nihon Shoki) which used a lunar calendar, and translated into our Gregorian calendar.
Around World War 2, this holiday was abolished, I think for reasons involving trying to seperate the church from the state (Emperors were considered to have divinity), but people apparently lamented its passing, and in 1966 it became a national holiday again, to celebrate Japan's founding. 建国 is pronounced "kenkoku" and means "founding of a nation" while 記念日 or kinenbi means "holiday".