A helpless opponent is someone who is bound, sleeping, paralyzed, unconscious, or otherwise at your mercy.
Regular Attack: A helpless character takes a -4 penalty to AC against melee attacks, but no penalty to AC against ranged attacks.
A helpless defender can't use any Dexterity bonus to AC. In fact, his Dexterity score is treated as if it were 0 and his Dexterity modifier to AC as if it were -5 (and a rogue can sneak attack him).
Coup de Grace: As a full-round action, you can use a melee weapon to deliver a coup de grace to a helpless opponent. You can also use a bow or crossbow, provided you are adjacent to the target.
You automatically hit and score a critical hit. If the defender survives the damage, he must make a Fortitude save (DC 10 + damage dealt) or die. A rogue also gets her extra sneak attack damage against a helpless opponent when delivering a coup de grace.
Delivering a coup de grace provokes attacks of opportunity from threatening opponents.
You can't deliver a coup de grace against a creature that is immune to critical hits. You can deliver a coup de grace against a creature with total concealment, but doing this requires two consecutive full-round actions (one to "find" the creature once you've determined what square it's in, and one to deliver the coup de grace).