A Cucco is a chicken that you will see roaming around towns and villages not only in Breath of the Wild, but also in almost all The Legend of Zelda games in the past.
In Breath of the Wild, whenever you hit a Cucco with any weapon, it may lay an egg. You can use its egg for cooking or for simply eating it to regain HP. You can find Cuccos around Kakariko Village and many other towns in the game.
Be careful of constantly hitting one as it may call other Cuccos to attack you. Being attacked by a horde of Cuccos is very dangerous as it can easily deplete yoru HP, so hit a chicken in the game moderately.