ROC curves are frequently used to show in a graphical way the connection/trade-off between clinical sensitivity and specificity for every possible cut-off for a test or a combination of tests. In addition the area under the ROC curve gives an idea about the benefit of using the test(s) in question.
In a ROC curve the true positive rate (Sensitivity) is plotted in function of the false positive rate (100-Specificity) for different cut-off points of a parameter. ... The area under the ROC curve ( AUC ) is a measure of how well a parameter can distinguish between two diagnostic groups (diseased/normal).
The AUC is the area under the ROC curve. This score gives us a good idea of how well the model performances. As we see, the first model does quite a good job of distinguishing the positive and the negative values. Therefore, there the AUC score is 0.9 as the area under the ROC curve is large.