To add to all these good answers, it also doesn't affect undead (the skull icon) which isn't important to know for jacks as noted above they are constructs so ignore ashen veil from that, but you might come across undead beasties if you play against minions (Boneswarm, Midas's feat, Maelok's field marshal ability).
Just to give a quick overview for future reference:
Ashen Veil affects living, everything is living unless noted otherwise. The two most common nonliving situations are Construct (Hammer Symbol) and Undead (Skull symbol) All jacks are constructs, as are the stone creations of Circle, the immortals of Skorne and most models of the Convergence. Undead are found in varying degrees in Cryx (most), Minions, Mercs and Skorne (least).
Therefore Ashen Veil is probably weakest against Cryx, stone heavy circle armies and the minion warlocks Midas and Maelok. It is probably strongest against the other Hordes armies.