The length of an object is not in general a fixed quantity. Many observers, all in motion relative to each other will generally disagree about the length of an object because of the length contraction of objects for rapidly moving observers. There is however one special measurement of length, called the proper length.
The proper length of an object is the length of the object on the inertial frame in which the object is at rest. In any other inertial frame, the ends of the object will move between measuring the positions of the ends of the ends of the object. This difficulty does not arise if the observer is at rest relative to the object, because the ends do not move relative to the observer.
With this definition the proper length of an object is unique.