A traditional term for the use of finite verbs uninflected for number or person with commands, wishes, suggestions, and hypothetical or counterfactual propositions. The 'present subjunctive' is the plain/infinitive form of the verb; the 'past subjunctive' is the general past form of the verb.

The subjunctive is the mood used to command, a wish, a suggestion, or a condition that is contrary to fact.

The board recommended that the motion be passed immediately.

If I were rich, I would live on Long Island.

Contrary to Old English, in modern English the subjunctive is distinguable from the indicative just for be, and the third singular person.
In modern English, the subjunctive mood still exists but is regarded in many contexts as optional. Use of the subjunctive tends to convey a more formal tone, but there are few people who would regard its absence as actually wrong.