I would say its the width of the exposed part of the sensor: you can have a slit that is 1mm move across the sensors, or 10mm, etc. Probably useful to write as a ration, 10% of the sensor width/height.
What Sandos said above.
Expanding on that.
A rolling shutter (Wikipedia) is a camera (or image) sensor technique that produces exposure times that can be effectively far faster (shorter duration) than the response time that can be achieved with a shutter alone.
This is achieved by exposing only part of the sensor at any one time.
If eg 20% of a sensor is exposed to light at any moment but the whole sensor is exposed at some point then the effective speed is 100%/20% = 5 x faster than the actual shutter time.
This is because 5 x less light reaches the sensor than if it was all exposed at once...
Not exposing the whole sensor at once can cause some "interesting" distortions.
Image below taken with an iPhone 4 with rolling shutter - from this
superb description of rolling shutter distoprtion effects
Alternative names are "roller blind" shutter and "dual curtain" shutter and "focal plane" shutter. (Their can be other forms of FPS but the dual curtain shutter is the most usual.
These names derive from the use of mechanical "curtains which move to first open the light path and then to close it.
In modern sensors it may be possible to replace one or both "curtains" with electronic turning on and off of the sensor elements. While a mechanical shutter will have a physical moving curtain the CMOS equivalent is simply active or inactive sensor elements.
To date the industry tends to imitate the mechanical arrangement so that a "wave" of active sensing propagate across the sensor. If this "wave" occupies 20% of the total width then the rolling shutter width will be 20% of the sensor width.
Once technology advances enough to allow the sensor portions to be enables and disabled semi randomly it will be advantageous to distribute the on and off areas. This would mean that there was no rolling shutter width per se.
The image below shows 3 examples of a rolling shutter in action.
In the left hand example the 1st curtain is falling and exposing the whole sensor area. It is not quite open as shown. The RSW (rolling shutter width) is the whole sensor width (5/6 as shown but it is likely to be going to fully open shortly).
In the middle image the 1st curtain is descending but being followed by the 2nd curtain 50% of the sensor width behind it (3 of 6 bars). Any location on the sensor will be exposed for only 50% of the time that it takes either curtain to cross the sensor so the effective shutter speed will be doubled. The RSW is 50% of the sensor width.
In the right hand image the 2nd curtain is following the 1st curtain only 1/6 of the total width behind it. Shutter speed will be multiplied by 6. The RSW is 1/6 of the full sensor width.
Here is the same image as above but animated so that the dual curtain action can be seen.
Wikipedia Focal Plane Shutter
From the above page:
Slow speed operation.
1st/red curtain opens fully before 2nd curtain starts.
Rolling curtain width is whole sensor width
High speed operation.
Red / 1st curtain starts to expose sensor but green/2nd curtain follows it before it has crossed sensor so there is a window or slit moving across the sensor. The rolling curtain width is the distance between red and green edges.