This value is the ability of your weapon to stagger enemies and leave them open to more consecutive attacks.
The impact level depend mostly on the weapon type and change depending on the weapon itself.
There is three main impact level : Low ; Medium ; High.
Arm gear can increases the impact level. But not above high.
Some Twin-rigged weapons have a "Very Low" impact level on their stats . While some Heavy-duty have a "Very High" impact level. It is not possible to reach the "Very High" rating if it's not innate to the weapon. However it is possible to enhance the impact with the RHINO gear set bonus and the implant Concussive Array v.3 (both can be stacked).
When under the effect of one of the above, the stats Impact will become blue, indicating its enhancement.
Crush, slash and thrust damages are affected by the stats of the player's weapon and the ennemy's gear.
Thrust damage seems to have a special function in very specific situations. For example, when the Bloodhound prepare his leap attack ("honk" noise), it can be interrupted by an attack dealing thrust damage.
Unfortunately, I have not find any other of those "very specific situations".
Dev explaining it : "Some weapons come along with elemental damage, a specific damage type which influences the overall damage for certain enemies."