Describe a situation that illustrates how you could be moving in one frame of reference but not in another?
You are travelling on a train:
With respect to a frame fixed on the ground you and the train are moving with a certain speed while in your frame, fixed to the train, you are not moving.
It is only when the train undergoes an acceleration (or deceleration) that you detect that something is going on. As the train, say, decelerates it seems that a Force is pushing you forward. Not existing a reason for the existence of this force you may conclude that you are in a moving frame without knowing it.