Sometimes crafty creatures and characters can choose to attempt more sophisticated, less direct means of gaining the upper hand in combat. Instead of taking a normal attack, they may opt to perform a Combat Maneuver. Like normal attacks, Combat Maneuvers require a Standard Action, but instead of opposing an Armor Class value with an Attack Roll, instead the success or failure of Combat Maneuvers is determined by a Combat Maneuver Bonus rolls opposed by the target's Combat Maneuver Defense score. If successful, the outcome is highly variable depending on which Combat Maneuver you were trying to perform, and while they tend not to immediately or directly deal damage, falling victim to a Combat Maneuver can be far worse than simply taking a hit in combat.
Combat Maneuver Bonus and Combat Maneuver Defense
Before getting into the details of the different Combat Maneuvers, first let's get the structure out of the way. A character's Combat Maneuver Bonus is much like an Attack Roll, although much less complicated; add your Base Attack Bonus, Strength Modifier and size modifier to get your Combat Maneuver Bonus. Naturally, this is checked by adding this bonus to a d20 roll in combat, and comparing the result to the target's Combat Maneuver Defense score, which is similar to Armor Class but for Combat Maneuvers.
A character's Combat Maneuver Defense score is equal to 10 + Base Attack Bonus + Strength Modifier + Dexterity Modifier + size. Other - typically secondary - bonuses to Armor Class also tend to add to a character's Combat Maneuver Defense, including Deflection, Dodge, Insight, Luck and Morale bonuses, but notably not including Armor, Shield or Natural Armor bonuses. This cuts both ways, however, as typical penalties to Armor Class also affect Combat Maneuver Defense. For example, just as buffs that add to Armor Class improve Combat Maneuver Defense, debuffs that decrease Armor Class will also lower Combat Maneuver Defense. In addition, any time you're denied your Dexterity or Dodge bonuses to Armor Class this also denies those bonuses to your Combat Maneuver Defense score.
To determine the success of a Combat Maneuver the attacker makes a Combat Maneuver roll in place of an Attack Roll, adding any bonuses they'd otherwise receive due to buffs or feats. If this roll meets or exceeds the target's Combat Maneuver Defense score, the attacker successfully performs the Combat Maneuver in question. Miss chance due to concealment applies to Combat Maneuver attempts.
Now that you know how Combat Maneuvers work in general, let's look at each of the Combat Maneuvers in Pathfinder: Kingmaker.
Note: Each of the following Combat Maneuvers has a feat - named after the Combat Maneuver - that you'll need to purchase before you can perform said Combat Maneuver. This is a bit of a departure from traditional Pathfinder rules, as you could normally use the Combat Maneuver without a feat, albeit while always provoking an Attack of Opportunity. To sweeten the deal, in Pathfinder: Kingmaker you receive a +2 bonus to Combat Maneuver attacks rolls and your Combat Maneuver Defense with the selection Combat Maneuver when you get the relevant feat.
The attacker attempts to push back - without injuring - a target five feet. If successful the target is pushed back five feet, plus an additional five feet for every five points by which the attacker's Combat Maneuver roll exceeds the target's Combat Maneuver Defense.
As the name implies, the attacker fights dirty, managing to either Blind, Entangle or Sicken the target. If the attacker is successful, the target will be afflicted by one such status for one round, plus one extra round for every five points by which the attacker's Combat Maneuver roll exceeds the target's Combat Maneuver Defense.
Disarming is a bit odd in Pathfinder: Kingmaker. Instead of knocking the weapon out of the defenders hand (after which they'd have to try to pick it up again), Disarm now does the functional equivalent. If the attacker is successful the target cannot use their weapons for one round, plus one extra round for every five points by which the attacker's Combat Maneuver roll exceeds the target's Combat Maneuver Defense.
If the attacker is successful, the target loses their Armor Bonus to Armor Class for one round, plus one extra round for every five points by which the attacker's Combat Maneuver roll exceeds the target's Combat Maneuver Defense.
A nasty Combat Maneuver which you'll unfortunately be on the receiving end of, the attacker attempts to knock the target prone. While not dealing any immediate damage, if knocked prone the target will have to stand up to continue fighting, which will provoke an Attack of Opportunity from all enemies that threaten the prone character. For every leg more than two, add +2 to the creature's Combat Maneuver Defense. Some creatures - such as oozes, creatures without legs, and flying creatures - cannot be tripped.