Bushido is a Japanese philosophy, roughly analogous to the Western concept of chivalry. It translates to "the way of the warrior."
Bushido is a "warrior code of honor" from the time of feudal Japan, which was to the Japanese what chivalry was to medieval Europeans. The values and ideals of this philosophy, adapted to a peaceful modern society, still influence Japanese culture today.
The seven cardinal virtues of bushido are Gi (righteousness), Meiyo (honor), Jin (benevolence), Makoto (honesty), Rei (respect), Chugi (loyalty), and Yu (courage). A warrior who follows bushido is expected to be self-disciplined, educated, and moral, and to demonstrate equanimity and filial piety at all times. Bushido also values protection and service -- two virtues very important to gargoyles.
The Ishimura gargoyles practice bushido, and often teach it to humans; Taro was one of their students, though not a very good one. After the Ishimura Clan's temporary capture by Taro and subsequent escape, they have begun teaching bushido to the humans living in Ishimura again, to strengthen their covenant with them.