Rurouni Kenshin is about Himura Kenshin who at the story's beginning is wondering Japan (in Tokyo atm, in the 11th year of the Meiji Era (1878) to be specific). He ends up at the doujo of Kamiya Kaoru and ends up staying there. Eventually the pair are joined by Myojin Yahiko, Sagara Sanosuke, and Takani Megumi. With this we have the main cast of the series (known as the Kenshin Gumi).
You may be wondering why Kenshin was wandering around Japan. 
During the Tokugawa era he was Hitokiri Battousai (if you're going 'huh what' here, basically he was an assasin for the Ishinshishi, one of the main fighting/ruling groups in Japan at this time). Many things happen during that time including the meeting of him and Yukishiro Tomoe who plays an integral part in shaping the Kenshin we know in the present day series time line. Kenshin, as one would assume, killed many people during his time as Hitokiri. Due to this (and also because of a major event/spoiler involving Tomoe) he swore to give up killing after he helped see Japan into the Meiji Era. He then began wondering Japan trying to help people in need with his Sakabatou (Reverse Blade Sword).
Going into any more detail on the above info will get us into uber spoiler territory and shall be covered eventually at White Plums my Rurouni Kenshin domain and fansite (or at least the beginnings of said fansite). It's named after Tomoe and is also home to the TAFL approved fanlisting for her (SQUEE!). Please visit that site from time to time (since I shall be slowly adding content to it) for more information on Kenshin, his past, his present, and the other Rurouni Kenshin characters I've mentioned in passing here.