R Squared - The coefficient of multiple determination is a statistical indicator usually applied to multiple regression analysis. It compares the accuracy of the model to the accuracy of a trivial benchmark model wherein the prediction is just the mean of all of the samples. A perfect fit would result in an R squared value of 1, a very good fit near 1, and a very poor fit less than 0. If your neural model predictions are worse than you could predict by just using the mean of your sample case outputs, the R squared value will be less than 0.
Do not confuse R squared, the coefficient of multiple determination, with r squared, the coefficient of determination. The latter is usually the one that is found in spreadsheets. See any statistics book for more details. Also note that sometimes the coefficient of multiple determination is called the multiple coefficient of determination, but in any case it refers to a multiple regression fit as opposed to a simple regression fit. Also, do not confuse it with r, the correlation coefficient.
You may also refer to the file RSQUARE.XLS provided in the NeuroShell 2\Examples directory. This spreadsheet explains why R squared is a better determination of model fit than r squared.
Note: R squared is not the ultimate measure of whether or not your net is producing good results, especially for classification nets. You might decide the net is OK by the number of correct classifications. For example, if you have a classification network with two outputs that generate output values of .6 and .4, the R squared value will not be very high.