I could have summarised the article below but it's late and I would have made a poor job out of it.
The Vox article, written by Alex Abad-Santos, briefly outlines the history of boof :
The history of the word boof, explained
There’s certainly no shortage of entries for “boof” on Urban Dictionary, the website that frequently comes up in internet search results for anyone Googling the term. But the key to the etymological puzzle behind the word is knowing how it was used in the 1980s, when Kavanaugh and Judge included it in their yearbook entries. And most of the available evidence seems to point toward it being a slang term for anal sex.
One of the most concrete examples of it being used, though in a different context, is in the cult classic movie Teen Wolf. The movie was released in 1985, a couple of years after Kavanaugh and Judge wrote their yearbook entries. In it, Scott (Michael J. Fox) has two love interests, the blonde dream girl Pamela Wells (Lorie Griffin) and the brunette girl next door, Lisa “Boof” Marconi (Susan Ursitti).
To some who were familiar with the term at the time, boof was slang for anal sex, hence the shock over Teen Wolf’s Boof.
There’s also another, totally different instance of “boof” being used in the 1980s. In 1981, two years before Kavanaugh’s yearbook entry, a man named John Paul Bonser was born. Bonser would grow up to become a professional baseball pitcher for the Minnesota Twins, Boston Red Sox, and the Oakland A’s. If the name John Paul Bonser doesn’t ring a bell even to baseball fans, it’s because he legally changed his name to Boof Bonser in 2001.
Bonser has said that his mother gave him the nickname when he was a child but never explained what it meant. “I don’t really want to know why, to be honest with you,” he told the New York Time in 2006. “I guess I had no reason to go up and ask her. I just left it at that.”
[…] in that message board conversation about Teen Wolf, a user who self-identified as being from the East Coast provided a corroborating account that “boof” grew out of “Bu-Fu (pronounced boo-foo), which was in turn short for butt fuck.”
Today, the slang version of the term has mutated slightly. It still involves one’s rear end, but it now appears to mean ingesting alcohol or drug through one’s butt. A simple search on Reddit, Quora, Urban Dictionary, or Twitter confirms as much (and yields multiple tips and tricks for doing it).
Vox Sep 27, 2018
In the cult movie, Risky Business, Joel, played by Tom Cruise, tells his friend Barry that…
Joel: Boffing and fucking are the same thing.
Barry: They are?
Joel: Ha-ha-ha. Yeah. What did you think it was?
Barry: I thought it was something else. You sure on this?
Joel: I'm positive.
Risky Business was considered on the best movies of 1983, it was acclaimed by critics and the public alike. Roger Ebert said at the time it was “one of the smartest, funniest, most perceptive satires in a long time”. The romantic comedy movie earned an impressive $63.5 million at the box office.
To get an idea as to how successful and popular Risky Business was,
we can compare it with two box office hits of the same year, The Big Chill ($56,399,659) and Scarface ($65.9 million). I'd wager that the movie earned a cult following among American teenagers, especially high schoolers, the movie was responsible for launching Tom Cruise's career.
In search of “boff”
Oxford Dictionaries define boff as
North American (informal)
1. Have sexual intercourse with (someone).
It seems to be imitative of blow, punch; an onomatopoeic word similar to ‘bonk’,‘pow’ and ‘whack’ found in comic books and related to the term hit. In fact, the idiom to hit on someone means to be sexually attracted to a person. According to New Collegiate Dictionary 2001, the first recorded usage of bof (but it's unclear whether it refers to blow = hit or sexual intercourse) is from 1937
The term boff […] This gentle-sounding word, with its suggestions of 'puff', 'buff' and 'buffer', next appeared as a convenient euphemism employed in US TV series, such as Soap, of the late 1970s and 1980s, where verisimilitude would demand a more brusque alternative. It is unclear whether the word is American or British in origin or a simultaneous coinage. It may derive from its nursery sense of 'to hit'.
Academic Dictionaries and Encyclopedias
Admittedly this is only speculation, and the term used in the movie was boffing but its morphological and semantic similarities with boofing should not be dismissed hurriedly.
Update on “boof” 10/10/2018
The controversy on the true meaning of boof continues online. This time an article from the Quartz, offers the following insight which was sorely missing in the Vox article.
Before quoting the relevant excerpt, I should explain I do not have a subscription to the OED (The Oxford English Dictionary).
According to the OED, a boof [in its original form] is “a blow that makes a sound like a rapid, brief movement of air.” The onomatopoeic word’s first known appearance in the English language, as the OED tells it, is an 1825 reference in the Supplement to the Etymological Dictionary of the Scottish Language.
Although unrelated to the modern slang meaning of "boof", its original significance is remarkably similar to that of “boff” mentioned by the New Collegiate Dictionary.