Arete is a measure of a Mage's enlightened will, his basic understanding of magic and his ability to control it. As the Mage's Arete increases, he begins realizing more that he is not a slave to reality – reality is a slave to him.
Arete is valued highly among the Traditions, as high-Arete Mages tend to be wiser, more in control of themselves, and more dedicated to their purpose. Of course, there are exceptions to this rule.
Whereas Spheres represent the breadth of a character's magical knowledge, Arete represents his raw magical power. Mages can never learn Sphere Levels above their Arete – trying to understand secrets before one is ready to wield them has had catastrophic results in the past.
Arete exists as a hazy in-character concept, a metaphor for enlightenment. A Mage might speak of his master as having strong Arete. He will never say "My master has Arete 4!" The numbers are to allow the players to keep track of how their characters are progressing. A Mage with Arete 2 may well seem more enlightened than one with Arete 3, but there is some block in his mind that prevents him from capably grasping that level of magic. Fortunately, although it is difficult to increase Arete, it is nearly impossible to decrease it. Once the walls are torn down, they are never rebuilt.
Most newly awakened Mages start with 1 Arete. Some, with traumatic Awakenings, start with 2 or 3 (though this often has the side effect of concurrent mental issues, often relating to the events of the Awakening). No mage may Awaken to higher than 3 Arete, anything further must be attained through Seekings. In any event, with an Arete of more than 5, in the words of Malkav: 'Reality doesn't like you because you exist.'