I noticed when you are sneaking around, the words "Hidden", "Caution", and "Danger" have brackets around them that seem to jump sporadically. What purpose do they serve exactly?
After reading the manual, apparently the brackets give you an indication of how successful your sneaking is.
The closer the brackets are to the word, the closer you are to being detected.
For example, when in the HIDDEN state, the closer the brackets are, the closer you are to being in a CAUTION state. When in a CAUTION state, the further apart the brackets are, the closer you are to returning to a HIDDEN state.
Hope this helps!
@Dom's answer is mostly right, but I think some clarification is in order.
The brackets actually indicate one of two things, depending on context:
How close you are to being discovered by a non-companion NPC, monster, or turret, due to factors like range, cover, and line-of-sight.
How aggressively enemies are seeking you.
When the brackets are farther apart, you're less likely to be discovered and/or you're closer to being "out of trouble". When they're closer together, you're closer to being discovered and to possibly being in trouble.
As for the terms within the brackets, here's a bit more clarification:
HIDDEN - Brackets will start at their most extreme separation. They will come together or separate to reflect your risk of discovery under current conditions, in relation to the thing that is most likely to notice you.
DETECTED - After the brackets have completely closed in from HIDDEN, you may be in a DETECTED state. This indicates that an NPC, monster, or turret has noticed you. This state most commonly indicates that the thing detecting you is friendly or neutral. However, it does sometimes appear when something hostile has just not yet chosen to engage in combat.
CAUTION - Something hostile is aware of your presence, and seeking you out for combat. In this mode, the separation of the brackets mostly indicates how aggressively they are looking for you. Close together, they're really sure you're there and are trying to hunt you down. Farther apart, they're starting to think you went away or "maybe it was just the wind". Once it reaches the furthest separation, you will transition back to HIDDEN.
DANGER - Fecal matter has impacted the rotating turbine. Hostile entities know you're out there, and more or less know exactly where you are. And they're trying to kill you. The brackets' distance may change according to the proximity or aggressiveness of the threat, but they mostly stay fully closed unless they're downgrading to CAUTION.
HIDDEN and DETECTED appear in the HUD's normal color, and they don't necessarily indicate the presence of hostiles. In mixed company, they also may not accurately reflect your stealth status with regards to hostiles.
CAUTION and DANGER appear red, and always relate to a hostile presence.