Serene is the state a Monk is the most powerful. When the state is activate, it will be indicated with a violet bar or circle close to your character on your game screen (depending on whether you use bars or arcs).
Monks almost always achieve this state but will lose it if party members are nearby and if they have 6 or more monsters adjacent to them. That means monks who are not in a party will always be serene.
While serene, a Monk's power is boosted as a doubler: virtues have their effect doubled, the autoattack bonuses from Ancient Shrines are also doubled, but the effect of Ascetic is not doubled.