What does the sneak crosshair state mean?
Flat line - Nobody knows you are there and nobody cares. Equivalent of HIDDEN in Fallout 3. You will get sneak bonuses.
Familiar eye - Someone is looking for you. Equivalent of CAUTION in Fallout 3. You also get sneak bonuses.
Detected eye - Someone can see you. Equivalent of DETECTED/DANGER in Fallout 3. You will not get sneak bonuses.
There is some information left out here that's important for a stealth character:
Even though the "DETECTED" eye is showing, you may still be hidden from any hostiles, because the symbol only means that someone has spotted you---this includes neutral characters, like guards, animals, even followers in certain circumstances. THEY could be the ones "detecting" you, while in fact you're in Stage 2 (hidden & being searched for) with respect to any red-radar hostiles.
The key is to listen for the audio cues: "You can't hide from me!" "Where did he go..." "I'll find you!", etc.
One strange thing about the "DETECTED" icon that I've not been able to figure out involves the "Shadow Warrior" perk at the apex of the Sneak tree.
Shadow Warrior gives you ~1 sec of invisibility when you crouch in the middle of combat, which breaks enemies' lines of sight and sends them immediately into Stage 2 (searching for you). Of course, if you try this right in front of them, they won't have to search for long...
The problem is, after I activate Shadow Warrior (even at range, around a corner), the sneak crosshair remains in the "Detected" Stage 3 state, even though I can hear those audio cues indicating that I'm not in Stage 3, but in Stage 2.
I'm not sure if this is a bug, or if I don't understand the higher-level Sneak perks as well as I should (spoiler alert: I don't. "Silence" baffles me; I have no clue what it means, because running instead of sneaking certainly does affect my chances of detection).
Internally, Skyrim uses Stealth Points to keep track of detection events. The player has a certain amount of Stealth Points at any given time, with a maximum of 100 and a minimum of 0.
When no enemy is able to detect you, the flat line is displayed
When an enemy could detect you, but hasn't yet, your Stealth Points begin decreasing. This is indicated by the eye opening. The more the eye opens, the closer your Stealth Points are to 0.
If you have less than 100 but more than 0 Stealth Points and something happens which makes the enemy no longer able to detect you, your Stealth Points begin regenerating back toward 100. The eye starts closing.
Any time your Stealth Points reach 0, you are Detected by anyone who is able to detect you at that time.
An important note is that enemies who are unable to detect you (for example, because you are around a corner) will not automatically realize you're there simply because your Stealth Points are 0, it only means that you have no grace period - the instant they can detect you, they will.
Also, you will not get stealth bonuses against anyone who has detected you. You will get stealth bonuses against anyone who has not detected you, even if you are detected by a third party at the time.
Source: Bethsoft Creation Kit