The ROC curve (or receiver operating characteristics) is a valuable tool to compare different classifiers that can assign a score to their predictions. In general, this score can be interpreted as a probability, so it's bounded between 0 and 1. The plane is structured like in the following figure:
The x axis represents the increasing false positive rate (also known as specificity), while the y axis represents the true positive rate (also known as sensitivity). The dashed oblique line represents a perfectly random classifier, so all the curves below this threshold perform worse than a random choice, while the ones above it show better ...