It is specifically a rolling shutter artifact combined with a wagon wheel effect. It is simply that the scene is only illuminated for a portion of the frame read. You can actually observe the same thing in still photography when you take a flash photo above the sync speed of the camera (because the flash is not long enough to cover the full exposure and there is no time the shutter is fully open).
With a rolling shutter, the image is captured sequentially, line by line, rather than all at the same time. If you had a global shutter, you would instead get a blinking due to some frames being completely unexposed and others being exposed. With a rolling shutter, you get partially exposed frames instead.
Since this occurs at an offset from the frame rate and the rate of the strobe and the shutter are different, the position of the line will shift slightly over time. This is known as the wagon wheel effect. If the rate of the strobe is slightly faster, the lines will move opposite the direction of the sensor reading as the light will go on or off slightly before the camera gets to scanning the line from the previous time around. If the frame rate is slightly faster, then it will move in the same direction as the scan as the lighting conditions will change on a slightly later read. If you get them in sync (or sync with a multiple) then it will hold position.
The wagon wheel effect is the exact same effect that can make plane and helicopter propellers appear to change speed and direction while they are spinning up. It is also the same effect used with a strobe for setting a timing belt on a car properly (by making a line on it stop moving up or down.)