AUC presents threshold invariance (no need to set a threshold as in accuracy) and scale invariance (if you scale all predictions linearly, but maintain ranking, then resulting auc is the same), which necessarily means that the AUC metric doesn’t depend on the chosen threshold or the scale of probabilities.
These properties make AUC pretty valuable for evaluating binary classifiers as it provides us with a way to compare them without caring about the classification threshold.
To plot a ROC (Receiver Operating Characteristic) curve, simply plot TPR as a function of FPR. That is,
true positives / total positives (recall) vs
false positives / total negatives (how many errors did you make in the negative case)
It can also be mathematically proven that AUC is equal to the probability that a classifier will rank a randomly chosen positive instance higher than a randomly chosen negative one.