The plus-que-parfait (pluperfect) describes an action that had already happened before another past action or point in time — the French equivalent of English "had done". It's formed with the imparfait of avoir or être plus the past participle: j'avais mangé (I had eaten), elle était partie (she had left).
It most often appears alongside the passé composé or imparfait to establish a clear sequence of past events: quand je suis arrivé, elle était déjà partie (when I arrived, she had already left) — the plus-que-parfait (était partie) marks the event that happened first. The same auxiliary choice (avoir or être) and past-participle agreement rules apply as in the passé composé.