I have has a mildly annoying morning.
I obtained a book, online, and I have discovered the pages were not cut.
That is, two pages were fused, never having been cut at the binder.
This volume is a reprint of a 1918 publication, so, not valuable.
But my efforts to slice thew pages apart at the bottom, with scissors, went poorly.
Torn pages.
So :
They are called “uncut”.
Unopened? Have not run into that for a while.
Use a knife
To open edges, cut with a dull knife held parallel to the plane of the paper. Cut out, away from the book.
I do not think that is precisely synonymous… an uncut (by guillotine) book might simply have rough edges
I think it’s correctly called “unopened”, whereas “uncut” refers to a book that hasn’t undergone a process of smoothing out the (opened) edges by cutting them. At least that’s what this pedant says.
Unopened is for pedants only. I’ve been a book collector for decades and have never seen it used on a modern book. Perhaps it’s standard terminology for pre-20th century books, where that might be an important factor in pricing or historical research on Shakespeare, but the only reason that article exists is to complain that everybody now uses uncut and that Folger exists - rightly - in a pocket of pedantry.
A sharp knife is good to use on uncut pages. One swift motion is best, so as not to leave the cut ragged. Scissors are not ideal because they are seldom sharp enough and also are too fat. A thin very sharp edge is better unless you have experience. Old fashioned letter openers are not as sharp and will work but probably not the first time. Just try not to saw at it.
What to use depends on the thickness and strength of the paper. One of my weirder experiences occurred in the rare book room of a university library. I had asked for a story weekly, a 19th century blend of newspaper and magazine that ran either “complete” novels or serialized them. They have to be brought out by staff.
Once I started to read I realized that several of the pages were “unopened.” I returned to the circulation desk and asked what to do. Finally, the head librarian appeared. She examined the weekly and then took out her business card and cut the crease. My jaw dropped but it worked fine.
Most newer books would not use that grade of paper or be that decayed and fragile. Books are meant to be read, so cutting pages is mandatory, IMO, something that needs to be said only because I’ve seen people with different views.
I’ve had only one uncut/unopened book. Once I was looking to buy a copy of Charles Darwin’s book on carnivorous plants. There was a new edition available but also a 100+ year old (non-first edition) copy for the same price of IIRC around $50, and thought it would be fun to buy the old one. when it arrived the entire thing was uncut and also tye paper had turned brittle from acid. So it wasn’t the smart choice.
Since the OP has been answered, I will tell a little story. In my last term in college I needed a literature course to graduate and signed up for an English novels course. We were given a list of authors and had to read a book a week and write a report. Anthony Trollope was on the list and I picked a book of his up at the library. The book had probably been in the library over 50 years and I was the first person to borrow it. Its pages were uncut. I took a kitchen knife and cut them. After I wondered if I should have done that; maybe the book was worth more uncut. But it was just in the ordinary stacks not rare book room or anything.
I can recall exploring the rather mouldy stacks of my undergrad university. I swear there were books in there that hadn’t been touched in 75 years. Made me wonder why they were still there.
Ex-library copies are worth far less to collectors. You did Trollope a favor.
Especially since when you were in college, Trollope was almost a contemporary. 
Books are meant to be read. You can’t read them until the pages are cut.
I would use one of my large kitchen knives, because the long blade would cut it easily.
And I’ve had books where one set of pages repeats and the next one is left out - obviously when assembling the folded and stitched sets they chose the wrong one. And one where one set of pages was upside down backward. Crap happens.
I had an Inspector Morse novel where most of the last chapter, with the reveal of whodunnit, was replaced with a repeat of chapter one. I was not happy!
Because eventually, someone might need them. I well recall needing to use, cite, and quote a 200+ year old American federal statute for a paper I was writing in law school. I can normally read American cites no problem, but this one had me stumped, and no matter how hard I looked, I could not find it in the stacks. So I asked the librarian.
“Ah, I can help you. Follow me.” So we went down into the basement of the law library, where she had to turn on the lights, and she found what I was looking for. I had to blow the dust off it, and there was a lot of dust.
For anybody curious, it was the Northwest Ordinance, (1787), 1 Stat. 51. According to the bookplate, the book was acquired from the US Library of Congress in 1931. The dust told me that nobody had needed it in years, probably decades, but it helped my paper. Which, I’m proud to report, I got an A+ on.
That’s why they’re still there.
I donated a copy of my PhD thesis to the library of my university, and when I visit (which is now only once every couple of years), I will sometimes go to the library and get that book. My hope is that someone using it every now and then would increase its chances of staying in the collection.
A memory.
I was wandering the stack at my Alma Mater, as a graduated former student may do.
I found a volume on references to Witchcraft and fairy-worship in Shakespeare, and I was intrigued. Or, maybe it was the dose of Intriguinol I had taken. (/s)
I sat down to read it.
And, I was puzzled. Many of the passages were out-of-step with modern Academia. I checked the publication date, and it was over 120 years old. I took it to the Head Librarian’s office, & urged it be added to the Restricted Section, not-to-be checked out.
Happened JBC, at Middle Tennessee State University.
I borrowed Thackery’s The Irish Sketchbook from the public library when they used to let you roam the Central Reserve Library. Some of the pages were uncut.
The Collected Works of J.V. Stalin slumbered safely on the shelves.
I’m guessing that many of these are old memories. Many - most? - academic libraries are so swamped with books that the older and unused volumes get moved to an offsite warehouse and have to be brought in when someone requests it, normally with a one to several day wait.
Public libraries usually have closed stacks that work the same way, although those may be on site. Much more culling is done is public libraries than in academic ones. Books that were only a generation old when I went to college but were superseded by more modern volumes that professors recommended, are now 100 years old and provide valuable insight into what those times were like, perfect bait for academic researchers. Attitudes on sex and race and class that were so common as to be invisible then now stand out as if in neon.