I found this question in my Google feed, meaning it's being promoted by the algorithm, meaning a lot of people are going to see it. While none of the other answers are outright wrong per se, I fear people who find this thread, especially all the comments, may take away an overall impression that they should be afraid to quote dictionary definitions in their writings. They should not be. I thus want to offer some thoughs and cite a few relevant sources that people can read and form their own opinions rather than just take these answers (including mine) on faith.
Before that though let me talk about ELU briefly. I'm not going to say too much here because I could easily delve into the legal advice territory if I'm not careful. Suffice it to say I think the site owners, in general, should probably consult an attorney (though they likely have already) if the copying and pasting of dictionary definitions by their users becomes widespread enough to attract the scrutiny of the publishers. There are potential arguments on both sides and I'm not sure the DMCA safe harbor is a silver bullet here, due to the unique nature of that site and its subject matter, and the amount of content moderation SE engages in.
That out of the way, I want to address the question's broader implications about quoting/citing dictionaries in one's own writing - which are completely different from that of the ELU site as a whole.
To put it succinctly, good faith quoting of an occasional dictionary definition - or any nonfiction source, frankly - with proper attribution, as part of an informational or persuasive piece (commercial or otherwise), fits the definition of fair use. Full stop.
How can I be so confident about this if fair use is ordinarily such a thorny and difficult topic?
1. The statute
Barmar already cited the statute (17 USC 107) and went through the 4 non-exhaustive factors so I don't want to repeat what he said, but I want to add the preamble to the mix:
[T]he fair use of a copyrighted work ... for purposes such as criticism, comment, news reporting, teaching ..., scholarship, or research, is not an infringement of copyright.
The 4 factors are then explicitly listed as non-exclusive (they "shall include"). The ultimate question of law hinges on the purpose of the use, and everything else in the statute falls into the "such as" category (i.e., it's illustrative rather than exhaustive).
Why, then, would one quote a dictionary definition in their writing? Are they trying to make and sell their own mini dictionary? Not likely (and not fair use). Are they criticizing or commenting on a new dictionary definition of a novel word? Not super common but it comes up occasionally, and when it does it is fair use by the plain language of the statute.
However, the vast majority of the time, someone quotes a dictionary definition
simply as a data point, in order to explain something (often something technical), to interpret some document or someone's words, to make an argument (often a legal argument!), or otherwise just inform a reader about something broader. It's usually simply offered as proof of a brute fact, i.e., a word's objectively accepted meaning, which cannot be expressed in any other way except through direct quotation. All of these purpose seem to pretty clearly fit those listed in the preamble.
What about attribution? The answers/comments claiming attribution is irrelevant here are oversimplifying things. True, once infringement is established, attribution is no defense, but that's not the question. The question is whether attribution is relevant to fair use (because if it's fair use, there's no infringement), and in my view it clearly is. It's evidence of your purpose. If you are trying to pass off someone else's work as your own, that could be evidence that your purpose is not fair. On the other hand if you properly quote and attribute the source, following ethical/scholarly/journalistic standards, that helps demonstrate a scholarly/informative purpose.
What about commercial vs. noncommercial? Well, it's right there in factor (1) of the statute, so to say it doesn't matter very much, without more context, is rather misleading and wrong on its face. Is it dispositive? Certainly not, but no one factor is. Fair use is found all the time in commercial cases, and not found all the time in noncommercial ones.
But does it matter to this particular hypothetical? I'd agree that it does not matter all that much, but only because the purpose argument is so strong that even purely commercial for-profit works should be covered. There are fringe cases I can imagine it mattering, but for run of the mill quotations in a nonfiction literary piece, I'd say not so much.
To briefly address the other statutory factors, I cover them in my hypothetical by simply assuming the writer is acting in good faith. I don't mean that subjective intent is a defense - it's not - but what I mean is a good faith actor here is simply not going to be pulling an unreasonable number of definitions from a dictionary, word for word, or trying to disguise their infringement behind some nominal piece of commentary, or doing the other things that would run them afoul of the other s.107 factors. But I'll get to this point a little more in (3).
2. Case law and procedure
Full disclosure, I looked for but could not find precedent about quoting dictionary definitions in informative non-fiction works. (I don't have access to Westlaw or Lexis, so if someone is aware of any relevant court decisions by all means please post the citations).
That said, I did find a useful summary article published by a law firm - Does Your Rule 12 Motion Based On Fair Use Have A Chance. (Incidentally, these kinds of articles are a common form of "soft" legal scholarship often done to draw attention to a firm's expertise. They can sometimes be very useful as a source to find actual case law when you don't have access to the pro research tools). I focused on the procedural question here because while I think it's rather obvious that the substantive question favors the quoter in our hypothetical, it doesn't mean all that much if blog authors and students have to live in fear of lawsuits that can't be resolved without discovery and massive expense.
While it's not common, it turns out that fair use defenses can be and are resolved through a motion to dismiss when the defense is obvious from the face of the complaint. As the article explains:
A review of recent court opinions shows that courts have granted Rule 12 motions where no discovery is needed to determine that the defendant’s use of the plaintiff’s copyrighted material squarely falls within the uses set forth in the preamble of the Copyright Act, namely, “criticism, comment, news reporting, teaching ... scholarship, or research.”
So, the suggestion, which has been made in this thread in more than one place, that a fair use defense always means a bruising protracted uphill battle for the defendant, is just not true. There are fair uses that are so open and shut that they will be outright dismissed by courts as a matter of law, if any plaintiff is foolish enough to bring them.
But again, to be fair, I don't know of precedents specific to dictionary quoting in the context of an informative or persuasive piece. There are ample precedents that dictionaries are copyrightable (at least to the extent they contain definitions not carried over from earlier editions that are now public domain) - see, e.g., Richards v. Merriam-Webster - and that wholesale copying of large portions of a dictionary is not fair use, but of course that's not the issue here.
3. Commonality of the Practice, and Common Sense
On my first day of law school, my contracts professor told us the most important legal principle you need to know is "The law is not an ass." 24 years later I have yet to see that principle fail.
Of course there are unjust outcomes and bad decisions all the time, but that's not what we're talking about here. A court decision holding a nonfiction author liable for quoting another nonfiction source in a responsible and ethical manner in conformance with commonly accepted practices would end nonfiction writing as we know it. Courts in the United States are not in the business of allowing outcomes that would defy all semblance of common sense or terrify the general public.
Quotation and citation are the backbone of nonfiction writing. This is drilled into us as students. We want pepole doing this, now more than ever when any idiot with a broadband connection can post whatever they want in black and white and disseminate it as widely as The New York Times (sometimes more widely). It makes for a more informed society. It's how we distinguish people who are just talking out of their butts from people providing legitimately useful information. It promotes the progress of science and useful arts.
Nonfiction authors, bloggers, students, journalists, etc., doing their work in good faith, are not going to get sued for quoting dictionary definiitons in their writings. If one does, an army of pro bono lawyers will descend upon the courthouse and put the travesty to rest quickly. Act reasonably, act responsibly, follow ethical practices. If your gut tells you you're near the line, consult an attorney. But please, do not be afraid to quote sources in your writing, especially on the Internet, where accuracy and responsible writing is needed the most.