Whereas the indicative presents an event as a fact, the use of the subjunctive often suggests that the person speaking or writing cannot guarantee that the event being mentioned is actually the case, or that it will definitely happen. The subjunctive therefore frequently expresses doubt or uncertainty.

Je ne crois pas qu’il soit prêt
I do not think he is ready

Il se peut qu’ils soient en retard
It is possible they will be late

Il est impossible qu’elle ait eu cette réaction
She could not have reacted that way

There are numerous occasions when the grammar of the sentence makes the use of a subjunctive obligatory. It is most often found in noun clauses introduced by a verb which expresses fear, doubt or regret, as well as after verbs which are used to give orders, express wishes, emotions or desires, or verbs which indicate that a particular event is only a possibility, one which might happen or might not.

On craint qu’il n’y ait pas de survivants.
J’ai bien peur que cela ne soit pas facile.
Il a toujours redouté que tout le monde apprenne la vérité.
Je doute qu’il revienne à temps.
Je souhaite qu’elle réussisse.
J’exige qu’il fasse des excuses.
Je voudrais qu’elle vienne.
Il se peut qu’il ait tort.
Il arrive qu’on ne s’aperçoive pas de ses erreurs.
C’est dommage qu’il ne soit pas venu.