The Area under the curve (AUC) is a performance metrics for a binary classifiers. By comparing the ROC curves with the area under the curve, or AUC, it captures the extent to which the curve is up in the Northwest corner. An higher AUC is good.
A score of 0.5 is no better than random guessing. 0.9 would be a very good model but a score of 0.9999 would be too good to be true and will indicate overfitting.
See also: Calculus - Integral