Symbolism, Imagery, Allegory
This is the perfect symbol for this play. Looming over the action from the very first scene is the skull of the woman whose murder starts the action. The skull belongs to Gloriana, Vindice's fiancée who was killed nine years before the play opens, thanks to a dose of poison delivered by the Duke in return for her refusing to sleep with him. Importantly, Vindice has carried the skull with him this entire time—so right away, it represents Gloriana's murder, Vindice's loss, the vindictive and lecherous ways of the Duke, and Vindice's obsession with revenge.
Pro tip: You don't lug a skull around for nine years without being at least a wee bit obsessed with revenge. And speaking of revenge, the skull doesn't just represent Vindice's desire to enact it against the Duke—it also helps Vindice do so. As he says:
[…] This very skull,
Whose mistress the duke poisoned, with this drug,
The mortal curse of the earth, shall be revenged
In the like strain, and kiss his lips to death. (3.5.103-106)
Vindice's desire to get the Duke back for killing his lady love basically amounts to tricking the Duke into kissing the poisoned skull, thereby using Gloriana's poisoned body (or what remains of it, anyway) to poison the Duke back. Lust inspired the Duke to kill her in the first place, and now Vindice uses this same lust to seek his revenge.
But here's the thing: The revenge doesn't stop there. Or, the revenge does, but Vindice's thirst for violence doesn't. We see him become a shell—you might even say a skeleton—of the moral self he puts forth during his revenge quest, turning his sights to Lussurioso despite Lussurioso not having taken the life of someone Vindice loves. If in killing the Duke we see Vindice driven by his heart, after he kills him, we can see him as all head—motivated by thoughts instead of real feelings.
In other words, while for much of the play the skull represents Vindice's loss and his morally supported quest for revenge, once he kills the Duke, the skull represents how hollow and emotionless Vindice has become.