Originally called 'fudai-no-shin (hereditary vassals),' fudai daimyo were daimyo who had been vassals of the Tokugawa clan for generations (the reason these daimyo were given this name was that a fudai, which can be written as 譜第 or 譜代 in Japanese, is a written genealogy proving one's ancestry), and were involved in all aspects of managing their master's affairs, from running his household to the supervision of estates and commerce within his territory.
もともと「譜第（譜代）の臣」と言うように、数代にわたり主家に仕え（譜第/譜代）、家政にも関わってきた家臣のことをさす。