A Bone Season is the decadal harvest of clairvoyants, those that live among humans with unseen but powerful abilities. Over a period of ten years they are rounded up and kept in the Tower to await their eventual exile.
The French word bonne means good. It was once known as the Good Season, the Season of Prospect, because the Rephaim could collect their reward (the humans to feed on).
The Bonne Season eventually developed into the Bone Season because humans see it differently. The Bone Season means bones, starvation, and death.