mean signed and unsigned (absolute) error

I'm trying to compare several computational chemistry methods with an experimental method, and some of the statistics of choice are the mean signed and unsigned errors, or MSE and MUE, respectively. The MUE is also called the mean absolute error (MAE).

I am trying to find a reference that shows the physical significance of these statistics, but I can't find a reference for them online or in a textbook. I've found an unreferenced article on Wikipedia for the MAE, but I'd like to better understand why I'm applying these statistics to my data and results, and what the limitations of these tests are. I can do the arithmetic to find the MSU and MUE, but I'd like to understand the significance of these tests.

My four calculated results sets contain twenty data points each, which I'm comparing with a twenty point experimental set.