Take Dissension's Stalking Vengeance, for example. Here's the art description provided to artist Anthony S. Waters:
This is basically a "revenge elemental" -- a large creature that delivers the rage of the fallen to those who cut them down. Design this creature how you see fit. Perhaps it's a giant cat-like creature whose fiery hide consists of faces of all kinds twisted in anger, for example. Let your imagination drive this one.
When an artist is given leeway like this, it's a sign of implicit trust in the artist's ability to convey the feel of the card. That trust was well-founded: here's the final art Tony submitted.
As you can see here, the creature is stepping among the graves of hundreds of fallen warriors. Many of the graves have death-masks or even the skulls of those buried attached to them. And the creature is none too happy about it—it bends down, perhaps to inspect a new addition to this ruddy graveyard, and as it does it roars in anguish.
Red creatures always do the same thing after roaring in anguish: they act on their urge to hurt somebody.
But this isn't just a sympathetic red beast feeling sorry for some dead friends. This is a manifestation of revenge itself—and as you can see, the art is full of visual cues to this. The creature's legs are actually composed of the gravestones of its fallen comrades (it is literally propelled by their deaths). Skulls roll in its eyes. Its body is lashed-together fragments of burial shrouds, bone, and coffin planks—and yet this is no black creature. The flush of red throughout the piece demonstrates that it's not about death, but about the reaction of rage following it.
This all ties to the mechanic, of course. When you put out your Stalking Vengeance, feel free to point out the exact person responsible for your creatures dying: your opponent.