This overview is based upon my own experience. Therefore it should not be considered as 100% true.

Aim:
Were your player hits the ennemy. Like in real CS you mostly aim for the head or the torso cause thats were you can do the most dammage with a single bullet.

Teamplay:
How your players play with each other. Imagine you have your players running from one end of the map to the other end and there are 2 different routes to take. Players with high teamplay might split up into groups and cover both roads.
Teamplay might also influence afterplant positions.

Handling:
Improves the ability of a player to throw his nade onto the position he wants.
This does not mean a player will hit his target all the time because he still has to know were the ennemy is if he doesn't see him.
I also noticed that the more handling a player has, the more hits he gets. I think this may be some kind of 'burst' simulation.
Aim will help to aim his gun but handling will help to control his gun when the player fires more than one bullet.
Therefore handling seems to be very important in mid range situations.

Playing IQ:
How 'smart' the player is. But like in real life an IQ of 100 isn't really high. It isn't in CSM either. Your players remain quite stupid :p
But still I think what PIQ does is give your player some kind of overview of the map with some probabilities of possible camp spots.
So when your player is cruising the map and he sees some boxes (cfr bombpot d2) he knows an ennemy might be hiding behind it. Then your player will have some idea of the area an ennemy might be situated in. Combining this knowledge with some awareness skill he might calculate the chance of an ennemy actually being there. And if those odds are high enough your player might throw a nade. Handling will then determine if the nade will hit that area.
I think PIQ might also influence afterplant positions although I have some doubts, cause they still seem quite stupid.

Quickness:
How fast your player reacts. When he sees an ennemy your player will have to aim and fire, the time between seeing and fireing is determined by quickness.
When a player gets shot in the back, the time it takes to react and turn is determined by quickness.

Determination:
How determined a player is to finish his job. A low determination can cause your player to fire once, then turn back into the direction of travel, then turn back to the ennemy to fire again. A high determination will make your player fire untill the ennemy is dead.

Awareness:
Gives some extra sense to your player. Players with high awareness will know the location of an enemy when they approach before seeing the ennemy.
Once your player knows an ennemy is comming he can already look into the right direction which saves some important time.

Creativity:
Influences things like strafing and the way your player is looking around when he's going on a defuse mission.

Patience:
When your players are camping and they see an ennemy they'll start to fire. But if they are patient they will remain in their position. If they are not they might leave their position hoping to kill the ennemy faster but exposing themselves.

Calmness:
Adrenaline might affect your players performance. You can see this as lowering all other skill values for instance.
Before a player reacts based upon all other skills I believe calmness comes into play to influence all skills. The lower calmness a player has, the more he drops in performance.