You may have noticed that in the Shop you can purchase not only regular chickens and cows, but also purebred ones. Purebred animals behave just like regular ones, but they give twice as much produce (eggs, milk, feathers, and meat) as them. They also look different.
By purchasing purebred animals you can exceed the limit of how many animals you can have. For example, if the maximum amount of regular chickens you can have is 5, you can also get 5 purebred chickens, which will bring your total amount of chickens to 10.