Combat Speed is how fast your character can fight in combat and swing in combat so your character can get moves in quicker before their enemies can. It is determined by a combination of your Dexterity, and Attack/Defense/Martial Arts Statistics, while also being heavily affected by the Weapon you choose to wield and the Strength level required to use it. Some Armour and Clothing types provide modifiers to it, making your character swing and block faster or slower depending on their gear.
Training your Dexterity and Attack/Defense skills are generally the primary method of increasing your Combat Speed, but maintaining a decent level of strength relative to your weapon is essential as well. The generally accepted rule is to maintain a Strength level of more than double the weight of your weapon in order to use the weapon effectively.
Oddly enough, Dodge is completely unaffected by Combat Speed. The movements seem to take the same amount of time regardless. Similarly odd, if they were affected, they appear to be set to look at the Martial Arts skill instead of Dodge as their other speed enhancing skill besides Dexterity.
The total value is based on a combination of your attack skill (Melee Attack or Martial Arts) or defense skill (Melee Defense), depending on whether you're attacking or defending, and your Dexterity. Roughly speaking, Dexterity will have a 1.5x greater effect on speed than the other skill in the pair will.
All weapons have a required Strength level to wield effectively, determined by the Blunt Damage of the weapon. In most cases this equals out to x2 the weight of the weapon (it is technically the Blunt Damage of the weapon multiplied by 40, but this will equal the same number as weight x2 in the majority of cases). If one does not have the required Strength to wield a weapon, this will result in a penalty to the speed. This scales as far as around -50% at 20 levels or lower than the required level. For every level above the 20 levels mark, the penalty will decrease by about 2.5% until you reach the required level.
Contrary to what has long been believed, damage types appear to have no direct affect on speed, or what skills are taken into consideration. As mentioned above, Blunt Damage affects the required Strength level of a weapon, meaning that in some cases Strength can be seen increasing the speed of a weapon, but in truth it is simply reducing the penalties instead. Assuming you have enough Strength to wield the weapon, extra Strength will have no affect on speed.
Item Related Edit
+Increases Combat Speed
-Decreases Combat Speed
Combat Move Speed Edit
Combat Move Speed is how fast your character moves around while in combat. It is often confused with the Combat Speed above, but is a distinctly separate and independent value. It is often modified by your Race, providing bonuses or penalties depending on which one your character is.
There is currently no know way to increase Combat Move Speed, beyond race selection. Though it is not impossible there is one that simply hasn't been discovered.
Hive Prince/Worker - 1.2
Hive Soldier Drone - 1.1
Greenlander/Scorchlander - 1
Shek - 1
Skeleton - 0.9
NOTE: This list covers playable races in Kenshi. Combat Move Speed for all races can be discovered in the Forgotten Construction Set.