Cover

To determine whether your target has cover from your ranged attack, choose a corner of your square. If any line from this corner to any corner of the target’s square passes through a square or border that blocks line of effect or provides cover, or through a square occupied by a creature, the target has cover (+4 to AC).
When making a melee attack against an adjacent target, your target has cover if any line from your square to the target’s square goes through a wall (including a low wall). When making a melee attack against a target that isn’t adjacent to you (such as with a reach weapon), use the rules for determining cover from ranged attacks.

Low Obstacles and Cover

A low obstacle (such as a wall no higher than half your height) provides cover, but only to creatures within 30 feet (6 squares) of it. An attacker can ignore the cover if they're closer to the obstacle than their target.

Cover and Attacks of Opportunity

You can’t execute an Attack of Opportunity against an opponent with cover relative to you.

Cover and Reflex Saves

Cover grants you a +2 bonus on Reflex saves against attacks that originate or burst out from a point on the other side of the cover from you. Note that spread effects can extend around corners and thus negate this cover bonus.

Cover and Stealth Checks

You can use cover to make a Stealth check. Without cover, you usually need Concealment to make a Stealth check.

Soft Cover

Creatures, even your enemies, can provide you with cover against ranged attacks, giving you a +4 bonus to AC. However, such soft cover provides no bonus on Reflex saves, nor does soft cover allow you to make a Stealth check.

Big Creatures and Cover

Any creature with a space larger than 5 feet (1 square) determines cover against melee attacks slightly differently than smaller creatures do. Such a creature can choose any square that it occupies to determine if an opponent has cover against its melee attacks. Similarly, when making a melee attack against such a creature, you can pick any of the squares it occupies to determine if it has cover against you.

Total Cover

If you don’t have line of effect to your target they are considered to have total cover from you. You can’t make an attack against a target that has total cover.

Improved Cover

In some cases, cover may provide a greater bonus to AC and Reflex saves. In such situations the normal cover bonuses to AC and Reflex saves can be doubled (to +8 and +4, respectively). A creature with this improved cover effectively gains improved evasion against any attack to which the Reflex Save bonus applies. Furthermore, improved cover provides a +10 bonus on Stealth checks.