What does mean and variance do in Gaussian noise?
Does mean increases the brightness?


As you add a constant mean to each pixels of the image you will get an image that has an overall higher average image pixel value. Since images are generally encoded with the maximum pixel value being white, you would get an image which is closer to white, and hence perceptually appears brighter.


  Does variance increases the amount of noise?


That one deserve a little bit more background. Indeed, quoting from Wikipedia:


  In experimental sciences, noise can refer to any random fluctuations of data that hinders perception of an expected signal.


So in that context, even adding or subtracting a constant value to the entire image could be coined as noise (especially if this makes the image too bright or too dark so as to make it harder to discern objects in the image). If on the other hand we focus our attention to what is commonly described as a "noise" effect then this typically refer to some kind of perceived "dots" that occurs due to somewhat large variations in pixel values in close proximity. Since the variance is directly linked to the variation in pixel values, it is clear that an increase of the variance would increase the amount of noise (in the sense of perceived quantity of "dots").