Simply put, the subjunctive is a mood used to express opinions, feelings and expressions of doubt or possibility. While it does exist in English, it is infrequently used and even less frequently taught so understanding its purpose can be quite challenging. It is used considerably more often in French, most commonly in a formal, written context.
One common example of its use in English would be “if I were you”; it theorises about a possibility rather than a certainty and so uses the subjunctive mood. A mood differs from a tense in that it refers to the nature of the statement rather than the time in which it takes place. As such, the subjunctive can be conjugated in other tenses and is not limited to the present.
When forming the subjunctive there are usually two central elements, although, as with almost every aspect of French grammar, there are exceptions. First, there are certain words and phrases that trigger the subjunctive, the majority of which end in ‘que’. Common examples include “il faut que” (“it is necessary that” or “one should [do such and such]”), “bien que” (although) and “autant que” (as far as).
The second component is conjugating of the verb after the trigger phrase in the subjunctive. Regular verbs are conjugated by taking the present-tense conjugation of the verb in the ‘ils’ form, subtracting the “-ent” suffix and adding the appropriate subjunctive ending. These are –e, -es, -e,-ions,-iez, and –ent for je, tu, il/elle/on, nous, vous and ils/elles, respectively. For instance, the verb “finir” (to finish) is “finissent” in the present, 3rd person plural form so “finiss-” is the stem used in the subjunctive form. So, “il faut que je finisse cet essai” means “I should finish this essay” ; it is an expression of opinion or purpose rather than of fact.