What Do Skewness and Kurtosis Represent?
This paper has a nice write up on those and many other measures.

For skewness:


  In terms of digital image processing, Darker and
  glossier surfaces tend to be more positively skewed than
  lighter and matte surfaces. Hence we can use skewness in
  making judgements about image surfaces. 


This is because skewness measures how "lopsided" the distribution of pixel values are.   

For kurtosis:


  In digital image processing kurtosis values are
  interpreted in combination with noise and resolution
  measurement. High kurtosis values should go hand in
  hand with low noise and low resolution. 


I'm not sure I agree with this.  Images with moderate amounts of salt and pepper noise are likely to have a high kurtosis value.