I've searched the 3 core books and I cant find one mention of Bounded Accuracy. Where is it, or is it just implied?
It was one of the major selling points of the edition during the open playtest process. One of the major complaints against both 3e and 4e was the “bonus treadmill,” where level-appropriate challenges increased in DC and AC at exactly the same rate that PCs bonuses increased, making it so that if you fell behind in terms of expected bonus progression, you were at a significant disadvantage. Furthermore, lower-level threats rapidly became completely non-threatening because they literally could not hit you and you could not miss them.I think it's come up in blogs or interview wherein the designers have talked about the math behind the game. Couldn't point you to specifics, though.
To address this, WotC proposed the idea of “bounded accuracy” in the new edition, which was really more like bounded target numbers. The idea being that difficulty of DCs and ACs would no longer scale based on the PC’s level. 10 is always easy, 15 is always moderate, 20 is always hard, etc. no matter what level you are. PCs would still gain bonus as they leveled up, but they would come much more slowly, so that your bonus never outstripped the d20. While a high-level character might have a bit of an easier time hitting a certain target number than a low-level character, the difference would be relatively small, and you would never reach the point where you couldn’t miss, or an opponent couldn’t hit you.
The primary intended effect of this change was to make it so that low-level monsters could remain a threat to high-level characters in enough numbers. In 3e, it doesn’t matter how many Kobolds you throw at a 15th level party. They just can’t hit the PCs, so they are not a threat. In 4e, they tried to address this by having different stats for different kobolds - so while standard Kobolds wouldn’t be able to hit a 15th-level PC, a special elite kobold soldier or whatever could. This was very unpopular with a certain crowd, so with 5e they decided to instead flatten the math. Now, one kobold may not be a threat to a 15th level party, but enough of them will be. This benefit also goes the other way - 5e characters can punch above their weight class by using numbers and clever tactics to their advantage, which 3e and 4e characters couldn’t because of how the math worked.
Finally, bounded accuracy was supposed to make it so that magic items with +X bonuses to hit or AC would be genuine bonuses. You wouldn’t “need” a weapon with a certain bonus by a certain level to keep up with the treadmill. In fact, magic bonuses would always put you ahead of the mathematical expectation. So those bonuses would feel like true bonuses, making things actually easier instead of keeping them from getting harder.
You don’t really hear about Bounded Accuracy much any more except from people who played a lot of 3e and/or 4e and participated in the 5e open playtest, because the concept isn’t really meaningful except in contrast to the math of those editions. The articles and blog posts on the subject have long been taken down, and I doubt WotC has much interest in talking about that stuff any more. The goal at the time was very much to win over people who disliked 4e. But these days, 5e doesn’t need to sell itself on being “not 4e,” so a lot of the design choices that specifically addressed common 4e grievances just don’t get talked about any more because they don’t need to be.