Wounding is an incredibly important part of Dauntless because it provides windows of opportunity to deal additional damage to a Behemoth, lop off a limb, and restrict a move-set. Unlike the Hammer (blunt weapon), it's actually anything that can slash which will cause a wound, with the War Pike causing the highest amount of Wound damage (that's the red damage against a Behemoth, not the yellow or grey). Wounds are represented by scars on a Behemoth's skin, where aether flows out of them. 

Each Behemoth has an invisible Wound bar, and simply put, the more Would damage you deal against a specific limb, it will eventually be sliced off. Slashing weapons deal +50% part damage to wounded parts, and Blunt weapons deal +25% part damage to wounded parts. Piercing weapons have their -25% part damage penalty removed once the part is wounded.

If you can, try to aim for the legs or tail, with Behemoth's who're weak indicating their soon-to-be wounded status by ever-increasing scar tissue. Continued strikes against the body part will then cause a wound and eventually a lost limb.

Finally, Perks that increase or deal wound damage include Acidic, Barbed, and Merciless. I'll let Xploit take it from here.