A non-juror is a person who refuses to swear a particular oath.
In British history, the non-jurors were those who refused to swear allegiance to William and Mary in the aftermath of the Glorious Revolution. This included Anglican clergy who were deposed for their refusal, resulting in the Nonjuring schism; it also included a number of laypersons.
In regards to French history, non-juror refers to those members of the Roman Catholic clergy during the French Revolution who refused to swear an oath of allegiance to the state under the Civil Constitution of the Clergy. These are also known as refractory clergy, refractory priests or, as appropriate, refractory bishops.