"It" being a new era in Twins history. In terms of running the operation, there have been two distinct eras: The Calvin Griffith years (1961-1984 or '86) and the MacPhail/Ryan years (1986-present).
Griffith transplanted a uniquely bare-boned, nepotistic operation from Washington to Minnesota. He was primary owner and served as his own general manager. A brother, Sherry Robertson, ran the farm system for years; two other brothers and a brother-in-law were also team executives. (The siblings were nieces and nephews of Clark Griffith, who had no offspring of his own; he formally adopted the oldest boy and the oldest girl but was guardian to the others as well.)
When Carl Pohlad purchased the franchise during the 1984 season, Howard Fox, one of the few non-relatives in Calvin's inner circle -- death had thinned his generation down down -- became general manager. He didn't hold the position long. Andy MacPhail was named general manager in 1985, spent 1986 getting a handle on things, and that offseason drastically reshaped the operation, bringing in Bob Gebhardt from the Expos as assistant general manager, Terry Ryan from the Mets as scouting director and promoting Tom Kelly as field manager.
And the Twins promptly won the World Series the next year (famous Gebhardt line: "We were just trying to get organized and we won the World Series") and did it again in 1991. Gebhardt left to become the first general manager of the Colorado Rockies. MacPhail left after the 1994 season to become president of the Chicago Cubs, and Ryan inherited the big job and held it, with the exception of 2008-11, when he stepped aside and Billy Smith was general manager.
Today Derek Falvey and Thad Levine are to be introduced as chief baseball officer (Falvey) and general manager (Levine). Presumably the operation is to get another face lift. We'll see if the new era is as long lasting as the first two.