Your End Game. When you hand in your resignation, it can kick off a bit of chaos__your position will need to be filled, but your duties will also need to be covered until they can replace you. As part of your resignation letter, it's a good idea to convey what your availability is during that transitional period.
Asking You to Stay Beyond Your Notice. In this situation, you won't necessarily get the promise of more money or a better title__but your manager will ask you, perhaps as a personal favor, to stay a few additional weeks or months until the company is able to hire and train a replacement.