This "ROC area", which you may also hear referred to as "area under the curve" or simply "AUC" is a measure of good your model is. You can read about ROC curves to find out more about it, but I'll tell you the basics:
You'd talk about it in the context of your model making decisions based on a threshold, e.g. when you've got a model that considers a sample "positive" or "negative" based on whether a probability or any other score output by your model is more or less than a certain threshold.
If you were to make a plot of the sensivity vs. the specificity for all values of the threshold, you get a curve. And the area under the curve is this "ROC area" that you're talking about. It'll be a value between 0 and 1. Generally, the higher the area (i.e. the closer to 1), the better.