Take a look at the screenshot below.
The left army is mine, sieging an enemy city. The right army is an enemy's army (same faction as the city I'm sieging) that I just defeated in a battle before laying siege.
At first I thought the red skull means that it (the army) contains the last leader of a faction, but this can't be true because I have other generals as well.
Best Answer
As mentioned by @5pike, the red skull symbolises attrition.
There are several reasons why an army or a fleet can suffer from attrition, here are some: