The past subjunctive is used for the same reasons as the present subjunctive - to express emotion, doubts, etc. The past subjunctive is used when the verb in the subordinate clause - the verb that follows que - happened before the verb in the main clause.
The past subjunctive may be used in a subordinate clause when the main clause is in the present tense:
Je suis heureuse que tu sois venu hier.
I'm happy that you came yesterday.
Nous avons peur qu'il n'ait pas mangé.
We're afraid that he didn't eat.
Or it may be used in a subordinate clause when the main clause is in the past tense. Note that if the main clause did not call for the subjunctive, the subordinate clause would have been in the past perfect, because the subordinate clause happened before the verb in the main clause. Therefore, the subordinate clause should technically be in the pluperfect subjunctive. But that is replaced by the past subjunctive in all but the most formal French.
Il doutait que vous l'ayez vu.
He doubted that you had seen it.
J'avais peur qu'ils soient tombés.
I was afraid that they had fallen.
Go on to page 2 to learn how to conjugate the past subjunctive.
Quiz: French past subjunctive
If you are having trouble understanding the French past subjunctive, thoroughly review my lesson on the subjunctive and then come back to this one. The only difference is the tense; usage is the same for the present and past subjunctives.