I have been reading some documents about meteorological data and many of them mention the second moment of wind velocity. I guess it has to do with the way the wind is changing but in such case I would call it a gradient... Therefore, what is it's correct physical representation?
The (statistical) variation is not the same as the gradient. The gradient is a measure how things change from here to a nearby point, or from now to a point in the near future. The variation, on the other hand, just says how often wind speeds of different magnitude happen.
For example: If the wind were to blow at exactly 30 km/h all the time, then the average wind velocity is going to be 30 km/h and the variation is zero. Conversely, if the average is 30 km/h and the variation is large, then the wind will blow at different speeds, typically quite different than 30 km/h, but so that the average is 30 km/h.
What's the importance in the context you're considering? If the variation were small, it would be fairly easy to design wind generators because they would only have to accommodate exactly one wind speed, which happens to be blowing all the time. On the other hand, if the variation is large, then you have to design wind generators so that they can produce electricity when there is little wind, when there is the average wind speed, and also when there is a storm. It's a bit like designing aircraft for (slow) take-off and (fast) cruise speeds -- it's complicated, as you can see with all of the flaps and levers moving on the wings of planes between start and cruise phase.