With the "Vibrance" slider it is possible to modify the saturation of the image in a more selective way (depending on the level of saturation of each colour). In other words, increasing the vibrance affects less saturated colours more, while decreasing the vibrance affects more saturated colours more.
In a way, the "Vibrance" slider allows you to balance the saturation of the image, equalising the saturation between the most and least saturated colours in the image.
Below you can see an example of the effect that can be obtained with this colour adjustment: