The best definition I could find is preserved in the Internet FAQ Archives:
Unsurprisingly, Loesch's supporters on Twitter enjoyed taunting her critics for their ignorance of the word, but their prescription seemed a bit off: "read a book maybe." I read lots of books, and it was a new word to me. It was also a new word to the six very literate members of my family (one Silent Generation, two boomers, three millennials)--five masters degrees and a juris doctor--who talked about this with me the other night. Five out of the six are big book readers, and the sixth reads widely online. The term was born on the Internet; it isn't too long a bet to say that it only exists there, and not at all in books.
fisking: n. [blogosphere; very common] A point-by-point refutation of a blog entry or (especially) news story. A really stylish fisking is witty, logical, sarcastic and ruthlessly factual; flaming or handwaving is considered poor form. Named after Robert Fisk, a British journalist who was a frequent (and deserving) early target of such treatment.
Some things from the early 21st century blogger argot entered general use; many did not. Tracking the roots of "Fisk," I located a legacy document that lists and categorizes locutions popularized by the website Little Green Footballs. It is revealing to examine: many of the ones that originated outside it are very familiar to me--asshat, Islamofascism, LOL/ROFLMAO/STFU, etc.--whereas I knew none of the ones that originated or potentially originated (like "Fisking") within this community.
But after all, as Dana Loesch the proud pajamarine would like the whole world to know, the NYT is just the moonstream media not to be distinguished from the Krazy Kos Kidz, a bunch of blue-diaper demonrats whose LLL just serves the interests of the Aloha Snackbars and the splodydopes and the Koranimals.
"What u haven't heard those words before? read a book maybe."