How could you be moving in one frame of reference but not in another?

Answer 1

Here's one example.

Suppose you're on a train. Now let's further suppose this is a very smooth-riding train and that the windows are covered up and you've never been on a train before.

As long as the train is going straight (no curves, no hills) and not accelerating or decelerating, it would be very difficult for you to tell you're moving relative to the outside world: everything in the train is moving at the same speed you are, or, to put it another way, you're all in the same frame of reference. That frame of reference may be moving 60 miles per hour relative to the outside world, but everything you can see or measure appears to be standing still.