The National and Imperial Seal of Japan was originally the Imperial Seal, and is called 菊の御紋 Kiku No Gomon in Japanese, which, literally, means "Noble Symbol of Chrysanthemum" or "Imperial Seal of Chrysanthemum" .
The Imperial Seal is used by members of the Japanese Imperial family. Under the Meiji constitution, no one was permitted to use the Imperial Seal except the Emperor of Japan, so each member of the Imperial family used a slightly modified version of the seal. Shinto shrines related to the Imperial family also use the relevant modified versions of the Imperial Seal as their seals, and some other Shinto shrines are not related to the Imperial family but are also permitted to use the chrysanthemum as a part of their seal.
The Imperial Seal became the National Seal when Japan modernized. It is on the cover of the Japanese passport, therefore solidifying its status as the National Seal.
The acceptable source of imperial wives, brides for the emperor and crown prince, were even legislated into the Meiji-era imperial house laws (1889), which stipulated that daughters of Sekke (the five main branches of the higher Fujiwara) and daughters of the imperial clan itself were primarily acceptable brides.
Imperial daughters and granddaughters, however, usually ascended the throne as a sort of a "stop gap" measure - if a suitable male was not available or some imperial branches were in rivalry so that a compromise was needed.
One, Empress Gemmei, was the widow of a crown prince and a princess of the blood imperial.