In ancient Greece, arete meant “goodness” or “excellence”. It’s related to araomai, to pray, and to aristos, meaning “the best.” That’s where the word “aristocracy” comes from. Aristocracy is the rule of the best people. So you needed arete to be an aristocrat.
Ancient Greek people thought of arete as meaning something like the US Army’s old slogan, “Be all that you can be.” It meant that you were being the best person you could be. So arete would mean different things for different people. In the Odyssey, Penelope has arete, because she is the best wife that a woman can be. But Achilles in the Iliad also has arete, because he is the best warrior that a man can be. Odysseus has arete because he is so clever, and thinks up effective plots. Athletes have arete when they win the foot-race.
Not only people could have arete – a well-built house, a beautiful piece of pottery, and a strong horse all had arete too. In Plato’s Allegory of the Cave, the ideal form of a thing is its arete, the goal that everything is trying to get to. As Plato says, arete is something you are always trying to achieve, but it’s always out of reach: it’s a goal.