Subjunctive is a term in the study of grammar. It labels one of the moods of the verb. The subjunctive is comparatively rare in English, although important in most other European languages, where it is a necessary part of verb use after certain subordinating conjunctions, etc. In English, the subjunctive is hardly used in informal and colloquial varieties, but is valued in academic writing. Quirk says of it that it "is generally an optional and stylistically somewhat marked variant of other constructions" - this means that to use it marks the user as a formally educated person laying claim to some respect. It is rather more frequent in American English than in Britain, even in formal British English.
Formally, the present tense inflections of the subjunctive are nearly always the base form of the verb. So the form is only different from the indicative mood in the singular: the 3rd person present subjunctive has no '-s'. The exception, as so often with verb forms, is 'to be': its present subjunctive is declined with be for all persons: 'I be', 'you be'; 's/he/it be', 'we be', 'they be'. The past tense of the subjunctive can only be seen as a separate form in current English in 'to be', and then only in the first and third persons singular. Here the forms are were where the indicative has was, as in the well-known formula 'If I were you'. (The past subjunctive is sometimes called the were-subjunctive for this reason.) Because the past subjunctive is more an expression of mood than of the time of an event ("I should be grateful if you would ..." is a wish for the future, expressed in a verb in past (here the subjunctive) tense form), a true past meaning has to be expressed in a past perfect form: "If I had known then what I know now, ..." (The formal, stylized effect may be enhanced by Subject/verb inversion to replace the conjunction 'if': "Had I known then what I know now,...")
The subjunctive expresses ideas that are less actual, certain or factual than the indicative: it is used "to denote an action or a state as conceived (and not as a fact) and therefore used to express a wish, command, exhortation, or a contingent, hypothetical, or prospective event". (OED). In other words, it expresses such ideas as doubt (as in "if that be the case,..."); certain kinds of wishing or hoping ("God save the Queen!" is a prayer and a wish; it is neither a statement nor a command); some forms of condition ("If he be single, let him have the flat"); and other similar states of mind. Commentators often refer to the 'hypothetical' as a root part of the function of the subjunctive.
Perhaps the commonest noticeable use of the subjunctive, other than some conventional formulae, is what Quirk calls the mandative subjunctive ('mandative' means 'communicating an order [or similar], persuading' and so on). This is the use of subjunctive forms of the subordinate verb in clauses introduced by 'that' after such main verbs as 'decide', 'propose', 'demand' and 'grant', along with certain equivalents that are not verbs. (There is a list of such verbs in Quirk, 16.32, and of some adjectives and nouns that take similar uses of 'that' + subjunctive at 16.72 (ii).) These result in such usages as "The judge directed that the prisoner be taken down [to the cells]", "The committee decided that the money be spent", and "Agreement was reached that peace be declared" ( a noun use); and "It is necessary that all factors be taken into account" (adjectival).
One of the reasons for the comparative scarcity of the subjunctive in English is no doubt its tendency to be identical in form with the indicative. A second is that its uses can very often be replaced by auxiliary verbs - and in informal English usually are. "I hope that it be so" [subjunctive] is the same as "I hope that it may be so" [auxiliary], and, more colloquially, "I hope it may" or "I hope it will"; "he prayed that it be a good day" = "he prayed that it would [or] might be"; and, in the mandative subjunctive, "The judge directed that the prisoner be taken down [to the cells]" can just as well be "The judge directed that the prisoner should be taken down [to the cells]".
The conventional formulae mentioned above include "Come what may" (~ 'Let whatever may happen come'); "Be that as it may" (~ 'Let that be whatever it is'); "If I were you" (an impossible condition, therefore properly the subjunctive rather than the indicative); "Be it enacted by the Queen's most excellent Majesty" (a clear order, in rather archaic formula); and "Suffice it to say" (~ 'let it be sufficient').