“You are more likely to notice details about people. Awareness will give more detailed information about them when you perform an Examine.”— Fallout description
“With Awareness, you are given detailed information about any critter you examine. You see their exact hit points and information about any weapon they are equipped with.”— Fallout 2 and Fallout Tactics description
Shows the HP, equipped weapon, ammunition type, and ammunition count of any characters, creatures, and robots when examining them.
“If additional information is what you crave, then this is a most helpful augmentation to your V.A.T.S. combat interface, as it allows you to see what a foe's resistances are and use weapons they are susceptible to.”— Fallout 4 Vault Dweller's Survival Guide description
While this will reveal resistances for an enemy (in addition to a crossed-out symbol for immunities), it will not display any special characteristics. The main example of this is that ghouls are listed as having 1000 radiation resistance, when in truth they have a special effect that lets radiation damage heal them, making the resistance moot.
Also, while previous versions of Awareness (and for Fallout: New Vegas, the similar Living Anatomy) also revealed the enemy's health, Fallout 4's version only reveals the enemy's level, which can sort of be used to approximate how tough the enemy is.
When taking the Aim minor action at a target within Close range, spot their weaknesses and can attack more efficiently. The next attack made against that target gains the Piercing 1 damage effect, or improves the rating of any existing Piercing X damage effect by 1.