The alert state indicates that guards are now on the lookout for the player. They are aware of his presence, and are suspicious.
How to Enter Alert State[edit]
Guards might become alert of Edward if he has a high Wanted Level and walks past them.
They also might suspect him if he fires a dart at them and misses, or attempts some other sort of attack and whiffs.
How to Exit Alert State[edit]
To exit an alert state, simply hide for a long enough time or bribe a town crier.