The term is often used to explain the nature of 5e in comparison to other, earlier editions. Is there a good description or explanation of what this actually does include and mean? And what is meant by saying something is breaking bounded accuracy?
For example, there is this question about what it means for to hit and AC, but does this also apply to skill checks, and if not, why not? The concept of bounded accuracy is normally presented to include all of attacks, saves, and skill checks.
Bounded accuracy is a design philosophy implemented to avoid some perceived problems from earlier editions. The name is a bit unfortunate as 'accuracy' mainly associates it with To Hit and Armor Class bonuses, perhaps bounded bonuses would be a more accurate term when speaking of this design principle in a more general sense.
In combat, bounded accuracy helps prevent one-sided fights with lower CR monsters. Keeping AC and to a lesser degree To Hit bonuses bounded means it is not always impossible for low CR monsters to avoid a higher level player's attacks nor is it impossible for the monsters to hit the players in return. This allows for more nuance in combat encounters because DMs can create easy encounters that still have some stakes to soak up resources and low CR monsters can now be used in greater numbers to actually make an encounter more difficult.
Out of combat, bounded accuracy / bonuses is designed around bounded skill DCs and to a slightly lesser extend skill bonuses. This bounding helps prevent skill checks becoming impossible for players with a lower skill bonus. This avoids players being sidelined and unable to contribute to an encounter because they don't happen to have the right skill proficiencies.
Both of these effects also lead to less pressure on player character to 'keep pace' as they level. For example, players don't have to worry about not being able to hit enemies later on if they don't invest in scaling their To Hit bonuses.
Breaking AC or DC bounds will have the largest consequences. Applying larger than usual numbers to them will start to reintroduce the problems bounded accuracy was designed the avoid, task can start becoming impossible unless to hit/skill bonuses were heavily invested in. It is likely the problem will be even more noticeable when reintroduced like this, because bounded accuracy works best when applied universally. Players do not have many ways to substantially buff their bonuses, there are exceptions like the expertise feature but the point of bounded accuracy is that these high bonuses should not be necessary to play the game and engage with encounters in a meaningful way. Your party should not be required to have a rogue with expertise in survival to even have a chance navigating dangerous areas succesfully.
Like mentioned already, there are features in the game that can be argued break bounded accuracy from the other end by introducing large bonuses. But as long as these large bonuses are not a requirement to meaningfully play the game, they do not reintroduce the main problem bounded accuracy aims to avoid (which again, is impossible tasks). This does not mean high bonuses are necessarily balanced, flooding the game with them will obviously make tasks meaningless and might even encourage breaking bounded accuracy on the other end by increasing ACs and DCs across the board.
Pepijn explained this well, but I'd like to add an example of what bounded accuracy is meant to avoid.
In fourth edition, to-hit bonuses, armor class, proficiency bonuses, and so on scaled roughly linearly with character level. This is sometimes called "level scaling" and meant that a first-level fighter had about the same chance of hitting a first-level monster as a twentieth-level fighter hitting a twentieth-level monster.
It also meant that a twentieth-level fighter would have a 100% chance of hitting a first-level monster, and a first-level fighter would have a 0% chance of hitting a twentieth-level monster*.
* Technically not quite 100% and 0% because of the crit rules; if you roll a nat 20 and it's still not enough to beat the target's AC, for example, you still score a normal hit. But that's not important here.
So if your 20th-level party wants to go take out a bunch of kobolds and goblins, you can't use the stat blocks you used at lower levels—there would be no risk, it wouldn't be especially exciting or fun. Instead, there are alternate stat blocks for use at higher levels, which have appropriately scaled bonuses and defenses, but are marked as "minions" (they have only one hit point but never take damage from missed attacks).
This worked well enough. But it could also be unsatisfying, because while the raw numbers went up steadily as you gained levels, the actual mechanics of combat didn't really. You still had to roll about the same on the d20 to hit, and you'd take out about the same percentage of the enemy's hit points. And, more importantly, you had to work to avoid falling behind the curve for any reason—you needed increasingly powerful magic items just to maintain the same odds of hitting a level-appropriate monster. If the wizard picked up a crossbow at first level but never put any effort into getting better with it, they would get worse at using it against basic kobolds, while their spells still have about the same odds of hitting.
5e decided to avoid this. If you're in a one-on-one fight against a single monster of appropriate CR, your odds of hitting will stay about the same. But now, even a 20th-level character should have a chance of missing a 1st-level goblin from the start of the game, or getting hit by them, and a higher-level character shouldn't get any worse at things they don't focus on upgrading. To accomplish this, all bonuses and targets are kept within a certain range regardless of level.
