Most lightning doesn't occur as just a single pulse of current. Rather, once the main discharge channel has been established, the actual visible bolt of lightning is generally observed to proceed as a series of pulses in rapid succession, over a course of many tens of milliseconds. After each pulse, the discharge channel remains partially ionized (and therefore conductive) for a period of time, so the next pulse largely just follows the same route, as does the one after that, etc.
So the main discharge channel is illuminated many times in quick succession.
If at the same time the wind is moving the discharge channel sideways (after all it's a column of plasma, and can be blown by the wind), then each successive pulse will be displaced a little from the position of the one that just preceded it.
If you have a camera with the shutter open taking a picture during this, then it records all of these successive strokes into the same image, so it ends up looking like a ribbon.
Does that make sense?
By the way, the best and most sensible explanation I've yet come across, as far as the actual process of how the discharge channel forms, and why there appear to be "stepped leaders" and so forth, is by Peter Thomson, and can be found here: http://www.peter-thomson.co.uk/tornado/Lightning.html
He calls this process a "reverse cascade", and his explanation makes much more comprehensive sense than for instance the fluff you can find about it on Wikipedia. If you follow Thomsons's reasoning, then it makes sense how you could have a succession of pulses of current, as different cloud regions are successively connected to the main discharge channel over time...