The past anterior or passé antérieur is a literary tense that is not much used in French nowadays. The form of the past anterior is much like the passé composé, except that the auxiliary is in the simple past rather than the present; i.e. j'eus parlé instead of j'ai parlé.
The use of the past anterior is very limited. It is not used in spoken French, and in written French it's generally restricted to subordinate clauses, to express a action or state immediately preceding the main clause. Usually the pedantic and old-fashioned-sounding past anterior can be avoided by rewording the sentence. Some French speakers will replace it with a passé surcomposé.
Examples:
A peine Louis XIV fut-il mort, le Parlement annula son testament.
Aussitôt que le duc d'Orléans eut prit le pouvoir, il libéra des centaines de prisonniers.
Lorsque Louis XV eut atteint sa majorité, la Régence cessa.