Zombies are special workers available when the Underworld Deity has been selected. To produce a zombie you need 20 devotion, an unburied corpse, and 100 Piety. This value never goes up, making zombies a far more efficient workforce to humans, since the "Food" cost, food in this example being the piety to spawn them, will never go up, whereas with regular workers, the more you have, the more expensive they are to produce at beginning of the game, whereas at the middle and late stages of the game, food production allows for large quantities of workers to be spawned.
Zombies also don't need to eat food, meaning, with enough dedication, you could wipe out your entire human population and instead just use zombies. To achieve this you'd need to have plenty of zombies, and a good amount of stored Piety. First, send a bunch of soldiers on a raid, and get rid of all your graves and apothecaries, and let the diseases kill all the humans. Then, use your Piety on all the dead bodies to make a large army of Zombies. You won't have to waste any manpower on food, but you will still need Farmers to produce Skins for Leather.
Zombies also don't suffer from unhappiness, meaning that no matter how much you overcrowd, they'll still work just as hard. This will be mildly irritating for a happy settlement of zombies, since they won't get a work speed boost. And since they also don't count as population, it makes reaching population achievements rather difficult. Since zombies are not regular workers, spawning them does not provide a possibility of receiving a Cat, which is a little annoying, but shouldn't be too much of a trade-off.