ROC (Receiver Operating Characteristic) curve plots True Positive Rate (TPR) vs False Positive Rate (FPR) at various thresholds.
AUC (Area Under Curve) measures overall classifier performance:
TPR (Recall) = TP / (TP + FN) - How many actual positives we catch
FPR = FP / (FP + TN) - How many negatives we wrongly call positive