This is an in-depth article describing inner workings of the game mechanics. Anyone not willing to spoil themselves or not liking boring mathematics, please skip this and read the non-spoilery summary on skills here.
There are three primary values which affect the attack strength of a character: damage, to hit value (THV) and hit speed. Damage is self-explanatory. Chance to hit the enemy is 100% / (DV/THV + 1), where DV is the enemy's dodge value, which is calculated from agility, size, burden state, etc. THV also affects the chance to hit weaker bodyparts like the head and the ability to block attacks. How many attacks you can do in a certain amount of time is proportional to hit speed. A skill bonus of X percent increases each by X%.
The total bonus to the attacking ability against a given enemy is however difficult to calculate, since for instance the bonus to real damage done against the enemy is greater than X%, since it is calculated by substracting 50-100% of the target bodypart's AV from the above damage. Sometimes you wouldn't do any damage without the skill, but with the skill you do, so the bonus percentage is infinite. Also, the bonus to real hit and block chances varies according to the enemy's DV etc.
There is a single value called danger value which is calculated through an extremely complicated formula effectively simulating the two creature's combat and calculating the ratio of the average time they need to kill each other. It would be the best way to tell the effect of the skill, but alas it is unique to each pair of monsters. It is the most important value used to determine the monsters which the game may throw at the player.
Since the bonus is so ambiguous and there are so many values affecting combat, we choose not to show too much exact info in the game. Strange floating point numbers calculated from a thousand sources would only scare players away. This is IMHO quite a realistic approach; in real life you have some rough estimate of your fighting ability but you can't know how much use it is against a certain enemy unless you try it out.
Conclusion: Weapon skill is very important in combat, but no one can know exactly how much. Personally, I never use the above formulas, but depend on my gamer's intuition.