Area Under the Curve (AUC) is a performance measurement for classification problems. It tells how much the model is capable of distinguishing between classes. The higher the AUC, the better the model is in distinguishing between classes.
Let’s take an example using logistic regression as a classification algorithm : To combine the False Positive Rate (FPR) and the True Positive Rate (TPR) into one single metric, we will first calculate the two former metrics with different thresholds (for example 0.00;0.01,0.02,...,1.00) for the logistic regression. We’ll then plot them on a single graph, with the FPR values on the abscissa and the TPR values on the ordinate. The resulting curve is called the Receiver Operating Characteristic Curve (ROC) curve, and the metric we consider is the Area Under the Curve (AUC) of this curve, which is called Area Under the Receiver Operating Characteristics (AUROC).
In the figure above, the blue area corresponds to the Area Under the curve of the Receiver Operating Characteristic. We present the ROC curve of a random predictor with the dashed line in the diagonal.