She and her sister Harmonia, goddess of concord, were known jointly as the Praxidikai (Exacters of Justice). As with many minor Greek deities, there's little or no real mythical background to Arete, who is used at most as a personification of virtue. The only story involving Arete was originally told in the 5th century BC by the sophist Prodicus, and concerns the early life of the hero Heracles.
At a crossroads, Arete appeared to Heracles as a young maiden, and offered him glory and a life of struggle against evil; her counterpart, Kakia (κακία, "badness"), offered him wealth and pleasure. Heracles chose to follow the path of Arete.
This story was later used by Christian writers, such as Justin Martyr, Clement of Alexandria, and Basil of Caesarea, use Prodicus' story, but Justin and Basil change Arete from a modest and attractive maiden into a squalidly dressed and unattractive figure.