War marks are granted to a village when they win a war. This happens even if your giants destroy the attacking army before it reaches the defending city.
A village with more war marks needs less greed to start a war and has a stronger army than a village with similar prosperity. This can lead to a greedy village spiraling out of control - the village fights a war, gains the mark, and loots, gets more greedy, fights another war, gets more loot, and so on.
A village can only have up to five war marks.
The easiest way to avoid gaining war marks on a high score village (for example for unlocking "calm") is to destroy all their potential targets (after collecting their ambassadors).
War marks can be helpful in creating a village that mainly runs on looting other villages, but this strategy needs great timing as you might lose all you have looted before the end of the era if you do not time this well.