Parentheses serve several specific functions, but their general purpose is to set a grammatical unit of content off from the surrounding text. The parenthesized material can range from a single letter, numeral, or other symbol to an entire sentence. (Because enclosing more than one complete sentence in parentheses overextends the digression, it is not recommended.) Here is a summary of ways to deploy parentheses.
First, a definition of terms: Parenthesis denotes a single parenthetical mark, but it can also refer to a digression, interlude, or interval enclosed in parentheses or other pairs of punctuation marks, such as commas, dashes, or brackets. The first of two parenthetical marks is an open parenthesis, and the second is a close parenthesis. The pair together are called parentheses.
A parenthesis of an entire sentence can be inserted within another sentence, but omit a period after the parenthesized sentence (However, an exclamation point or question mark is acceptable!) to avoid confusion. (A complete sentence may also follow the terminal punctuation of the preceding sentence; in that case, include a period—or another terminal punctuation mark—immediately before the close parenthesis.) An incomplete sentence within parentheses is not punctuated with a period, but, again, an exclamation point or question mark is allowed.
When providing an explanation or an example, the additional information can be enclosed in parentheses. Note in the following sentence how a parenthesis of a parenthesis should be formatted. (The abbreviations e.g. [“for example”] and i.e. [that is”] generally precede such information in formal and scholarly prose; in more casual contexts, the phrases are employed.) This is general American English style; British English style (and legal style and style for some other contexts) is parentheses within parentheses.
Parentheses enclose the abbreviation of an acronym or initialism after the spelled-out name of an agency, company, or organization to inform the reader about how the entity will be identified on subsequent references: “The National Association for the Advancement of Colored People (NAACP) was founded in 1909.” (Note that the article the is not repeated in the parenthesis, but it should precede the initialism when it appears again.)
Parentheses are used to enclose a note when a reader is directed to a cross-reference or when a writer glosses (presents a brief definition of) a term, provides a citation for a quotation or a fact or figure, points out that he or she has used italics to emphasize part of a quoted passage, or otherwise annotates a quotation.
Note that the location of the parenthesis in the following sentence is awkward: “Consider whether a ‘risk expert’ should serve on the committee (i.e., someone with a background in risk management or oversight relevant to the nature of the organization’s operations).” Parenthesized annotation, just like additional information enclosed in a pair of commas or dashes, should immediately follow the relevant word or phrase, as here: “Consider whether a ‘risk expert’ (i.e., someone with a background in risk management or oversight relevant to the nature of the organization’s operations) should serve on the committee.”
Back-to-back parenthesis is acceptable, but this can be avoided by combining two pieces of information into one parenthesis divided by a semicolon or by reorganizing the framing text to separate the two parenthetical comments.
When the items in a run-in list (a list appearing within a sentence rather than formatted vertically) are numbered, they should be enclosed in a pair of parentheses (not with a close parenthesis only)—as in “The three types of rocks are (1) igneous, (2) metamorphic, and (3) sedimentary”—but numbering is seldom necessary.
Use parentheses in moderation; excessive deployment of the symbols can give text a cluttered appearance (note their ubiquity in this post) and result in an obstacle-ridden narrative flow. Often, a pair of commas will suffice in their place, and dashes are appropriate when abruptly interjecting additional information, especially when the writer wants to give an impression of sudden interruption rather than unassuming interpolation.
From: Daily Writing Tips