What follows draws heavily on Mark Nichol’s “8 Types of Parenthetical Phrases” (16 Jul 2012, http://www.dailywritingtips.com/8-types-of-parenthetical-phrases/) at the excellent Daily Writing Tips site.
A non-essential phrase that can be inserted at the start, in the middle or at the end of the sentence, a parenthetical phrase serves one of eight functions. (By way of an example, the opening phrase here is a parenthetical — an appositive, in fact — as is “by way of an example.”) Because it is grammatically inessential, it should be set off by commas.
1. Absolute phrase: An absolute phrase (a noun/pronoun + a participle) modifies the entire sentence, acting like an adverb. It is “absolute” because it is grammatically independent of the rest of the sentence.
Jane stayed up late, writing her report.
2. Appositive: An appositive is a noun or noun phrase that is juxtaposed (“apposed”) to another to rename it, i.e., to identify or explain it, or supplement its meaning.
If you, an experienced hiker, had trouble, how hard will it be for me?
3. Aside: An aside is a phrase or clause that qualifies a sentence. (Compare interjections, which are “content-less.”) It can also be placed within parentheses or between em dashes — like so — to intensify its effect.
Her friend, I hesitate to say, has betrayed her.
4. Free modifier: A free modifier adds detail about the subject (“I” here). It is “free” because it can be positioned wherever it sounds best.
I stood up and, brushing off my pants, continued along my way.
5. Interjection: An interjection — here, strictly speaking, an exclamation — injects into the sentence information (or rather, an emotional cue because it is “content-less”) about the writer or speaker’s state of mind.
Well, what do you have to say for yourself?
6. Introductory phrase: An introductory phrase precedes the main clause to provide contextual information.
On vacation, I had an epiphany.
7. Resumptive modifier: A resumptive modifier “extends” a sentence by repeating a word and adding detail, i.e., resuming the sentence.
She was exhausted, more exhausted than she had ever been before.
8. Summative modifier: A summative modifier extends a sentence by summarizing an idea expressed in the main clause (hence “summative”) and adding detail about it.
We headed toward the summit, the goal we had anticipated all week.
(To remember the eight functions, think “the AA aficionado made amends with the IRS for his intemperance.”)