Kikoku is Japanese for "Demon Cry" or "Demon Wail". It's derived from 鬼哭, the first kanji being 'oni' (ogre or demon), and 'KOKU' (wail, cry, weep, etc). The 'ON' reading for 'oni' is KI, which is where KIKOKU is made. It was also a Japanese movie from 2004.
There is a misconception among some that the meaning of 'Kikoku' is Japanese for "Return to one's homeland"; this is derived from an actual word, and it is correct (shown in the kanji 帰国 , meaning 'return country' respectively). However, this isn't the kanji the relic katana uses.
Originally wielded during the Shadowreign era by Kupalu-Harupalu.
See Kikoku/Plot Details for more background information.