In Japanese, Hiten Mitsurugi-ryū is written 飛天御剣流. The first two characters, pronounced "hiten," refer to an image specific to Buddhist temples of a heavenly being in flight. The following two characters, which are read "mitsurugi," make up a name rather than a word. Individually, 御 means "honorable" and 剣 means "sword." Finally, the last character simply connotes a way or a manner.
In-fiction, Kenshin learns the Hiten Mitsurugi-ryū from a swordsman named Hiko Seijuro XIII (his twelve predecessors the prior masters of the sword style). However, Hiko Seijuro XIII's story significance is considerably greater than merely acting as Kenshin's teacher. Rather, Hiko is Kenshin's surrogate father, and even turns out to have given Kenshin his name. The Hiten Mitsurugi-ryū, then, is not just a manner of wielding a sword but part of the legacy that Kenshin's father figure passed down to him. This backstory is briefly touched upon in the third "Rurouni Kenshin" movie, "The Legend Ends," and, of course, explained in greater detail in both its anime and manga incarnations.
