To segue is to move smoothly from one song, idea, activity, or state into another, without a hard stop. A band segues from one song into the next. A speaker segues from a small story into the real point. You can also use it as a noun: “That was a smooth segue.” It started as a music-score word, from Italian for “it follows”: play the next bit with no break. Now it is ordinary in talk about shows, podcasts, and conversation. People even say “nice segue” with a little smile when you change the subject well — or with irony when you do it badly. Though actually, in careful music writing it still has the old job (go on at once, no pause); in everyday English the idea is the smooth join, not the sheet of paper. Say it SEG-way.