The ROC curve shows every possible tradeoff between false positive rate and true positive rate. The AUC summarizes overall performance in a single number. Drag the threshold and compare models.
AUC is the probability that the model ranks a random positive sample higher than a random negative. It's threshold-independent: a single number for the entire curve.
Caveat: with heavily imbalanced classes, ROC curves can look deceptively good because FPR is diluted by the large negative class. Precision-recall curves are often more informative there. See the class imbalance guide.