Introductions of new storylines. Some stock examples might include a character having a new job (or losing one), a character gets a new love interest (or an existing relationship either ends or enters a new phase), children entering a new school, the core group of characters move to a new home (or hangout, etc.) ... and the list goes on.
Often, one or more of these stories will introduce a fundamental change to a particular show. An example is Archie Bunker's Place, where Archie's wife, Edith, died and the characters deal with her death. Subsequent episodes had Archie adjusting to life as a widower and re-entering the dating scene.
In the case of game shows, the introduction of new (or revised) rules, new bonus games, rules concerning prizes (such as what can be won), and/or new models.
The show airing at a new day and/or timeslot, either to improve sagging ratings or - if the ratings are high - to anchor a line-up of new and veteran programs.