The namesake of puroresu heel stable Kaientai DX, Kaientai was a naval force created from a shipping company called the Kameyama Shachu, founded by Ryoma Sakamoto in Nagasaki in 1864. The Kameyama Shachu is often credited as being Japan's first corporation.
Kaientai began life as the fear of a young man living in an isolationist society confronted by the outside world. Sakamoto was living in Edo, now known as Tokyo, when, on July 8, 1853, Commodore Matthew Perry's "black ships" first sailed into Edo Bay. The appearance of Perry's intimidating ships followed by his demands for a treaty permitting trade jarred the Japanese people, who had no navy of which to speak. Sakamoto felt fear, envy, and hatred of the foreigners who had demonstrated such might, and decided that Japan should have its own fleet of ships.
In 1862, Sakamoto went to assassinate Katsu Kaishu, a high ranking officer in the government who commanded the ship sent to the US by the shogun for the purposes of signing a treaty between the two nations. Sakamoto believed that Kaishu was giving in too easily to the Americans' demands, and that he was a lackey of the shogun. Kaishu was aware that Sakamoto intended to kill him, and so he presuaded Sakamoto to listen to his own side of the story. Upon hearing Kaishu's ideas on foreign policy, which included a strong Japanese navy as well as trade, Sakamoto felt ashamed and begged Kaishu to allow him to become his follower. Kaishu assented, and in April of 1863, he convinced the shogun to establish a naval academy in Kobe, with Sakamoto as head of the school. Sakamoto recruited his friends who were of lower class as well as ronin from across the land and trained them in the handling of ships.
In 1864, the Kobe naval academy was shut down due to rebellion in western Japan. Sakamoto took 20 of his friends from the school and created the Kameyama Shachu. At first, they had no ships and had to rent a ship from another clan to transport goods. They got a break, however, when an associate of Kaishu's from the Satsuma clan contracted out the handling of their ships to the Kameyama Shachu because Sakamoto and his group were more highly skilled than the clan's own members. The Kameyama Shachu's management of the Satsuma clan's ships was imperative in mending the breach between the Satsuma clan and the Choshu clan, which eventually led to the dissolving of the shogunate and the reinstatement of the emperor.
In 1867, Sakamoto reorganized the Kameyama Shachu into the Kaientai, or "Naval Auxiliary Force". The Kaientai was used as the naval force for the Tosa clan, and was instrumental in establishing the precedent and force of international sea law. Sakamoto wanted to make sure that the foreigners, who were already members of the international naval community, understood that Japan would fit in well with the rest of the world, and honor their laws.
I apologize if this writeup seems oddly more about Kameyama Shachu than about Kaientai, but almost every source I found had a slightly different variant on what, officially, was to be called Kamayama Shachu and what was to be called Kaientai. I finally decided that the Sakamoto Ryoma Memorial Museum's nomenclature seemed the most plausible and meshed the best with what other information I had. I'm posting this under Kaientai as that name will be searched for far more than Kameyama Shachu. Moreover, anyone looking for Kameyama Shachu will likely know that it is associated with Kaientai.
I've done my best with what information I had, but concise, accurate information on Japanese history written in English is not easy to find. If you find any factual inaccuracies here, I will be happy to fix them, as they are likely just the product of a scarcity of quality information. Thanks.
Modern History. http://www.google.com/search?q=cache:FN6BC01j5KoC:www.columbia.edu/itc/eacp/japanworks/ teachingaids/japan/japanworkbook/modernhist/perry.html+%22commodore+matthew+perry%22+japan&hl=en&ie=UTF-8
Note: For the preceding link, the original webpage was unavailable, but I was able to view the page through Google's web cache.
Kyoto National Museum. http://www.kyohaku.go.jp/tokuchin/ryoma01/ryomae.htm
Ryoma Sakamoto. http://www.baobab.or.jp/~stranger/kochi/ryoma.htm
The Sakamoto Ryoma Memorial Museum. http://www2.net-kochi.gr.jp/~kenbunka/ryoma/english1.htm