Status, the prestige of a werewolf when interacting with others and the spirit world. Some wear their past deeds as spirit brands or markings, but even if not visible the renown of a werewolf represents their place in the hierarchy of Uratha society and should be heeded. Werewolf renown is based on 5 virtues, Purity, Glory, Honor, Wisdom, and Cunning. These are a rough interpretation of power and standing.
As of Werewolf the Forsaken Second Edition, Renown is more closely linked to acquiring Gifts. Furthermore, werewolves can 'flare' their Renown and voluntarily take a Renown Condition. Renown Conditions make your character act much like the stereotype of her Renown, which makes it easier for another character to manipulate and challenge her by gaining bonuses. Once someone uses that bonus, the werewolf can resolve the Condition to gain automatic success rolls equal to dots in Renown involving the Renown's Auspice's Skills. (Source: http://theonyxpath.com/renown/)