When is a 1-in-3 SAT clause satisfied?
A 1-in-3 clause consists of three literals. It is satisfied if exactly one of these literals is true. For example, if the three literals are $\bar{x}_1,x_2,x_3$, then the three truth assignments (for $x_1,x_2,x_3$) which satisfy the clause are $(F,F,F)$, $(T,T,F)$, $(T,F,T)$.