What does each skill represent? I don't believe the rules give a description of what they do. Here is Assur's description.
Attack - How good is your warrior at attacking? Note that your attack is modified by your opponents defenses and various other things, but this is one of the easiest skills to understand. Can I hit my opponent? Countered by defense and parry.
Decisiveness - This skill was added later in development It is believed to be a primary contributor to determining who attacks first. That is the only thing I would say it for sure does. And even in that, it is only one of many factors and someone with way lower decisiveness can attack before someone with much more due to those other factors.
Defense - This skill determines how well a warrior avoids an attack. High Activity level also helps if you rely on defense skills to win. (Though high activity level is good for many/most warriors).
Initiative - This skill is primary in keeping your attacks going, one after another. It also plays a huge role whenever there is a pause in the fight. Which warrior is going to attack next? Countered by Riposte.
Parry - This skill determines how well a warrior parries an attack. Note that it is possible for warriors to slip past parry with high attack, but this is the other primary defensive skill.
Riposte - As far as I know, this skill is only for taking the initiative from your opponent. When used, it always follows a successful parry/dodge with a line of text reading something Riposting warrior feints an attack, trying to disrupt the rhythm of the fight.
In terms of importance, decisiveness is HUGE early on. Parry, also, is enough to win fights with by itself early on. The balance of the game is very nice, though, and all of the skills are important in some form or fashion. However, as your warriors advance higher and higher in the game, the ultimate importance of the skills eventually becomes:
DEFENSE > ATTACK > PARRY > DECISIVENESS > INITIATIVE > RIPOSTE.
-- Assur