Short Definition
AUC ROC summarizes how well a classifier ranks positive examples above negative examples across thresholds.
Intuition
It measures ranking quality before choosing a specific decision threshold.
Technical Definition
ROC AUC is the area under the receiver operating characteristic curve plotting true positive rate against false positive rate.
Example
A risk model with higher ROC AUC tends to rank actual risky cases above non-risky cases more often.
Common Misunderstandings
AUC ROC does not choose the operating threshold for you.
It can be misleading under heavy class imbalance or asymmetric costs.