A Cuckotte is the games version of a chicken. They become available to be bought, pre-named, from 'Animal Lady' infront of you're barn after you complete act one and restore the farm.
They can be talked to, to check how they're doing. They can be fed produce by putting crops you have harvested in the 'Feed Box'
After some time you'll be rewarded for your efforts by eggs, which can be sold for 30G each, or Synthesized.