Site: http://www.ridgebackpress.com/heroes/shinsegumi.htm
If you just want the jist of it:
The Shinsengumi were recruited by the Tokugawa Bakufu to take care of the radical Choshu (pro-revolution/modernisation against Tokugawa) which was causing havoc in Kyoto. Basically a police-force to restore peace (ironically by violence).
Shinsengumi = pro Tokugawa
Choshu = pro revolution/anti Tokugawa
Hope that helped, but I'm sure you're all Japanese history experts...