What is the subjunctive?

The subjunctive is a  'mood', like a tense, it changes the conjugation of the verb.  It is used after certain phrases such as 'il faut que' (it is necessary that) and bien que (although) e.g. 'il faut que j'y aille' (it is necessary that I go there/I have to go there).  The subjunctive is also used when expressing emotion: 'j'ai peur que', 'je veux que', 'je suis content(e) que'.  It is used when expressing doubt 'je ne crois pas que', similarly it is used after 'il est possible que' as this is describing something uncertain.