A zombie head is involved in the quest A Clockwork Syringe. After you have defeated the Barrelchest mk II, the Zombie head will be on top of a barrel as an NPC. You will have to interrogate it, after which you will pick up the zombie head, making it will appear as an item in your backpack. Doing this causes the head to say, "Ye can't treat someone like this! Argh, there be fluff in the bottom o' your bag! It be gettin' in me nose!"
You should take it with you to talk with Bill Teach.
There is an option to chat with the head whilst it is in your backpack, although it will not say much.
Destroying it will cause it to reappear as an NPC in your player-owned house. Destroying the head gives the message, 'You place the head on uneven ground, and it rolls off in the direction of your player-owned house.'
If you accidentally lose or destroy the zombie head, make sure you leave your house, and when you left click the portal, there will be an option to enter called "A Clockwork Syringe". To recover the head, make sure you enter the POH with this option.