A proper frame, or comoving frame, is a frame of reference that is attached to an object. The object in this frame is stationary within the frame, which is useful for many types of calculations.
For example, a freely falling elevator is a proper frame for a free falling object in the elevator, while the surface of the Earth is not.
Proper frames can be inertial as well as non-inertial as in the example above.
References
Proper frame Wikipedia(Text) CC BY-SA