what does it mean to have a decorrelated colour space?
edit: to be clear this answer describes why Lab can be described as a decorrelated color space. This does not imply that decorrelation is the main benefit of using Lab (see many answers on why Lab is useful)

If you plot all the RGB colors of a standard RGB image of the natural world you will notice something (see below), the values tend to fall on a diagonal line that isn't one of the axes of the color space.

In fact if you know the red and green values of a color in RGB color space you could make a good guess as to the blue color, it would be the blue that makes the point fall near that clustered line. This is because the values are all very correlated, they are good predictors of each other.


  As I conceive it, CIE Lab is decorrelated means that there's an independence between channels, if for example the value of l* grows bigger, this doesn't necessary imply that the values of a* or b* increase too, but so is the case in rgb I guess. So, what am I missing


So as you can now see, as the values of one RGB dimension increase, the others are also likely to increase.

As it turns out, that clustered diagonal line running through the RGB cube represents the luminance dimension.

In CIE Lab, that luminance dimension we see in the RGB cube as a diagonal running from (0,0,0) to (1,1,1) has been made into one of the axes of the color space. If you know the a* and b* values of a color you still don't know much about the L value. The CIE Lab dimensions are decorrelated from each other because they don't predict each other.