Soak is a number that reduces the amount of damage received from a certain source by that amount.
There are many ways of getting Soak Values and almost all of them involve activating a skill or just wearing Armor, innate or not. You may notice a whole bunch of different numbers being listed when you look at these armors. That would be the Soak Values, the numbers that decide which type of damage receives which amount of reduction. So if a certain armor has 4 listed under Impact, it means that any attacks made by any weapon that deals Impact damage will be reduced by 4. Unless the target bypasses soak entirely with a skill or the damage would be reduced to 0 or less, in which case the hit will deal a minimum of 1 damage.
A negative soak, which is usually caused by curses, will work in the same way. If a certain character has -2 listed under Impact, it means that any attacks made by any weapon that deals Impact damage will be increased by positive 2 (i.e. reduced by negative 2).
Remember that you can see the damage type when you swing at people and they swing at you, to help you get a feel of which armor to prefer.
10 Impact character
Let's say an Infernal Behemoth with the skill Chitinous Armor gets hit. The many attackers have gathered around him and are pelting him with various objects and stabbing and slashing at him. As mentioned, however, this Behemoth has a skill that gives him armor. If someone were to hit him with a weapon that hurts for 10 Impact damage, he would deal 10 - 4 = 6 damage. This is because the Soak Value of the Chitinous Armor for Impact is 4.
9 Piercing Void Walker
Someone else comes at him with a gun that hurts people for 9 Piercing damage and he or she is also a Void Walker with the skill Precision of the Assassin. What this means is that normally the Behemoth would take 9 - 7 = 2 damage. However this certain skill reduces all Soak Values to 0 if the Void Walker attacks with certain weapons. He is lucky his Firearm triggers this soak bypassing and therefor he deals 9 damage to the Behemoth.
3 Impact Mortal
Another person comes by, this is a mortal who can only punch or kick this, in hopes of one day being able to do the same, but in a much more powerful way. He hits the Behemoth with his Fist that hurts people for 3 Impact damage. He now deals 3 - 5 = -2 damage. Does this mean the Behemoth heals for 2 Hit Points? Well, no, that would be crazy. It just means that the person attacking him has not enough damage to overcome the Behemoth's Soak Values. However, as mentioned before, it is vital to remember that any damage that would be reduced to 0 or less by Soak is instead set to 1. Therefore, this mortal still manages to hurt the Behemoth for 1 damage.
10 Acid Mortal
Let's just say the Void Walker gave the mortal a weapon that hurts people for 10 Acid damage. Would he be better off than just using his fist? Let's see, shall we. The mortal hits the Behemoth with the weapon. He is now dealing 10 - 9 = 1 damage. Which is just the same as if he were hitting him with his fist! The mortal kindly thanks the Void Walker and considers keeping it for people who do not have this much Soak against that particular damage type.