Star Trek: Discovery has finally explained why nobody ever talked about Michael Burnham or the USS Discovery. When CBS first launched the Star Trek prequel series, it caused a great deal of confusion. The show introduced a brand new character into Star Trek lore, Michael Burnham, Spock's adopted human sister. What's more, the Discovery was using a revolutionary new technology known as the spore drive, allowing it to jump through space in an instant.
How could this possibly fit into existing Star Trek canon? Spock has been a major recurring character over the years, so surely he should have mentioned Michael sometime, especially given she was such a key player in the Klingon War. And the spore drive is technology that hasn't even been hinted at before; if the Federation possessed spore drive technology back in 2256, why didn't it become standard? Had Voyager possessed a spore drive when it was kidnapped by the Caretaker in 2371, it would have been able to return to the Alpha Quadrant just moments after completing repairs. Star Trek: Discovery's showrunners had long promised that season 2 would resolve all these continuity problems, although frankly it seemed like a stretch.
However, the Star Trek: Discovery season 2 finale, "Such Sweet Sorrow Part II," pulled it off. It saw the Enterprise and Discovery locked in pitched battle against the forces of Control, the rogue artificial intelligence whose very existence threatened the future of all sentient life in the galaxy. Should Control manage to acquire the sphere data, it would be able to subvert its programming and become genocidal. There was only one way the Discovery crew believed this future could be avoided; to jump into the future themselves, taking the sphere data with them. The crew of the Enterprise then lied to Starfleet, claiming Discovery's spore drive had overloaded and destroyed the ship. It was a clever deception; the spore drive was experimental technology, the one other ship built with a spore drive had suffered a catastrophic failure in Star Trek: Discovery season 1, and Stamets - the only scientist who understood the spore drive enough to argue the point - had been on the Discovery.
But Spock went one step further. He argued that the threat of Control could not be allowed to recur, and that in order to lessen the chance of that all knowledge of the USS Discovery should be struck from Starfleet's records. Everybody who knew anything about the ship should be sworn to secrecy; they'd never be able to talk about the Discovery, the spore drive, or the battle against Control. Michael Burnham's name would be quietly erased from records. And Spock would never be allowed to tell anyone about his sister. From Spock's point of view, this was a masterful strategy; it meant nobody would ever research the spore drive and work out that the Enterprise crew had been lying. Starfleet would be happy to oblige, given that it allowed them pretend Control had never existed, and they'd not come within a hair's breadth of causing galactic extinction. Had the truth become public, they'd have had to admit to the existence of Section 31, so the secrecy spared the Federation public embarrassment and a major political scandal.
It's all eminently logical from an in-universe perspective, and it neatly explains why Burnham and Discovery haven't been mentioned in Star Trek canon before. To even acknowledge Burnham's existence would be to commit an act of treason. Meanwhile, the spore drive technology would be forgotten, viewed as a scientific dead end pursued by a scientist whose name would be lost in obscurity. Now it's in the future, but before the jump, Star Trek: Discovery cleared up all the confusion.