Understanding weapon system in Neverwinter Nights

The basics that you need to understand are Dungeons & Dragons concepts, as that is what NWN is based off of. Specifically, D&D 3rd Edition.

First off, combat happens in what is called "rounds". In 3rd edition, each round represent six seconds of time, so ten rounds would be a minute. At first, each class only gets one attack per round, and it's represented by their base attack bonus. So every class has the same attack speed at level 1. For instance, take a look at the Monk:

Level   Base Attack Bonus
1st     +0 
2nd     +1 
3rd     +2 
4th     +3 
5th     +3 
6th     +4 
7th     +5 
8th     +6/+1
9th     +6/+1
10th    +7/+2
11th    +8/+3
12th    +9/+4
13th    +9/+4
14th    +10/+5
15th    +11/+6/+1
16th    +12/+7/+2
17th    +12/+7/+2
18th    +13/+8/+3
19th    +14/+9/+4
20th    +15/+10/+5

At 8th level, you see +6/+1. That means they get two regular attacks, one at +6 to hit, the second at +1. At 15th level, they get another one.

This can be altered by some attacks, and notably, dual wielding means you get an extra attack per round, with a to hit penalty for both attacks. This penalty is reduced if the off-hand weapon is classified as a light weapon, or is balanced. To prevent confusion, dual wielding doesn't give you an extra attack per regular attack; it's just one extra attack. At 8th level, you would have three attacks, not four.

There are some other skills that give you an extra attack for that round, such as Flurry of Blows, but that is your entire attack for the round; you can't use it twice, once for each attack.

Base Critical Threat is based on the weapon you're using. Normally, the way critical hits work is that you first roll a twenty sided dice to see if you hit or not. If you roll a number within the Critical Threat Range, you have the potential for doing a critical hit. You roll another to hit roll, and see if that attack would hit the monster. If so, congratulations! You've done a critical hit! Your damage dice are multiplied by the critical damage on the weapon. One thing to note is that if your second roll wouldn't actually hit the monster, then it's not a critical hit, but you still hit the monster. Roll normal damage dice.

Here are some examples:

A sword has a Base Critical Threat of 19-20/x2. This means if you first roll a 19-20, you have the potential of critting. Roll again. If this roll with your to-hit bonuses would hit, you crit, and you roll your damage dice. Some people roll the regular weapon damage and just double it, some people roll twice as many dice. Either way works.

An axe has a Base Critical Threat of 20/x3. For this to crit, you have to roll a 20, and then roll again to hit the monster, but if you do, the damage is tripled.

There's a bare bones intro to combat in D&D. That should allow you to make some more sense out of the numbers you're seeing on weaponry.