From MangaHelpers:
During the era of the Tokugawa shogunate, there existed 12 samurai families that served under the emperor. They were called the "Tokugawa Jyuni Shinshou." Each of these samurai families passed down generations of each of their own unique martial art styles, and their mission was to protect the peace brought about by the Tokugawa shogunate.
Kuroshima Kotetsu, our main character, is the younger of the siblings in the Kuroshima family. The Kuroshima family is one of the 12 Shinshou families. Kotetsu will be in-line to succeed the next position as the master of the family, or so it was supposed to be until the invasion of the Black Ship. The invaders aboard the Black Ship brought with them weapons with enormous power, crushing the Japanese government. Kotetsu will now have to become stronger and fight for his beloved country and save the Japanese people.