A parenthetical is a nonessential sentence interruption-- when a sentence takes a quick detour from its normal pace and gets interrupted. Parentheticals are essential for both narrative writing (where they can pop in and give expository detail) and in academic writing  (where they are used [and often required] for source citation and elaboration). Unlike, say, a conjunctive adverb or modifying phrase, which provide additional information in a smooth way, parentheticals are meant to be abrupt in style. There are five types of parentheticals:  

1. An appositive phrase

An appositive is a single word that renames a noun prior to it (My dog Smuckers likes to eat ants). An appositive phrase is a string of words that does the same thing (If you, the self-appointed king of cool, can't get a date, what chance do I have?). Notice that appositive phrases break up the sentence flow and need to be surrounded by commas.

2. An aside

An aside is a statement that acts as an apology our explanation-- something a person might mutter under their own breath for their own purpose. An example: "Sarah is struggling (bless her heart) with even the most basic concepts." Since asides are not meant to be heard by all in real dialogue, they are punctuated within parentheses. 

3. A mid-sentence conjunctive adverb

We are used to conjunctive adverbs coming at the start of a sentence (Finally, I had a clown in my life). But what happens when, say, a conjunctive adverb is inserted in the middle of a sentence (like the word 'say' in this one)? That is, in fact, a parenthetical, and it gets surrounded by commas.

4. Nonrestrictive relative clauses

Relative clauses are dependent clauses that modify nouns and come in two flavors: restrictive and nonrestrictive. Restrictive relative clauses are essential to the meaning of the sentence and, when spoken, are smooth (The man that married my aunt dresses likes to dress like a woman). Nonrestrictive relative clauses, however, interrupt the sentence flow and act as a parenthetical (The man, who likes to dress like a woman, married my aunt). Nonrestrictive clauses are always set off by commas.

5. Explanations and comments

When an author wants to use a parenthetical to explain or comment upon an event or fact, they can do it in two ways-- with emphasis on the additional comment or explanation or without emphasis. If the author doesn't want emphasis, he or she sets off the comment with parentheses: Charlie met his wife at the seaside peer (where, incidentally, his father met his mother). The focus is still on Charlie though we have another expository idea. If an author wants to comment within a comment (meaning that he or she wants to use parentheses within a parenthetical [which occasionally happens]), the inner set used square brackets instead of round parentheses. Remember, end punctuation always goes on the outside of parentheses (meaning commas, periods, and the like).

If the author wants to emphasize the additional information, he or she uses a dash: Uncle Charlie--the most kind and generous of my three uncles-- was never a rich man. Note the difference between a hyphen (-) and a dash (--); hyphens are a single short line and combine while dashes are two short lines and separate.

SO WHY SHOULD I USE PARENTHETICALS?

Parentheticals make writing more dynamic and interesting by breaking up the regular syntax (which can get plodding and dull). They make pace vary-- sudden breaks and stops make writing sound more like actual vocal conversation and its irregular cadence. Authors, many of whom are not all that good at their craft (*cough* Twilight *cough*), can make a pointless and plotless text engaging through use of parentheticals. It also gives an author more flexibility in addressing a topic and adding information by, well, allowing information to be added essentially anywhere in a sentence.