|Jinmu-tenno, from Wikimedia Common|
National Foundation Day is on Feb. 11th every year. On this day, it is said that the first Japanese Emperor, Jinmu-tennou, established the new country in 660BCE (before common era), placing the original capital in Yamato. However, this actual date is uncertain. There are no records of his life or his reign, and indeed, there aren't any actual, firm, verifiable records of any ruler until the 29th Emperor or so. In fact, most modern historians and archeologists aren't even sure if he actually even existed himself, or if he was a historical composite figure of many legends and myths that became widely known and accepted. Curiously, Jinmu-tenno was born on the first day of the first month of the Chinese lunar calender, on Feb. 13th, 660BCE (much the same way various religious figures of the West were all born on the same date, which happens to coincide with celestial activity; see Christ, Mithra, Attis, and Horus).
Regardless, this is the date that is traditionally held today for the event, established during the Meiji era in 1872. There are some very intriguing political reasons behind the establishment of this holiday. Meiji-tenno was fighting claims regarding his legitimacy as Emperor after the Tokugawa shogunate was overthrown, and establishing a holiday that would link him with Jinmu, son of the Sun-goddess Ameterasu, in the eyes of the public would ensure his stay on the throne. Originally, the holiday was established as Kigensetsu, "Empire Day", on January 29th- the same year as Meiji-tenno implemented the national change from the traditional lunisolar calendar to the Western Gregorian calender. However, because of the original date, no one paid attention to it and saw it as only the usual Lunar New Year. A year later, in 1873, he then moved it to February 11th, but never disclosed how this day was calculated. Kigensetsu became one of the four major holidays in Japan until the 1940s, when it was temporarily abolished after WW2 due to it's extreme Shinto-based, nationalistic overtones. Ironically, Feb. 11th of 1946 was the date General MacArthur approved the draft version of the Japanese Constitution. Kigensetsu was re-established during 1966, this time under the modern name of Kenkoku Kinenbi, in order to once again unify a broken country and to show national strength and patriotism.
Another interesting note: "kenkoku" is a double-entendre word, similar to the way "shi" works. "Kenkoku", said one way, means "National foundation". Said/written another way, it means "Detestable nation". I am certain that many an essay has been written on the subject using this play of words.