Animals are commonly selectively bred for various characteristics, including:
Cows, goats and sheep that produce lots of milk or meat
Chickens that lay large eggs
Domestic dogs that have a gentle nature
Sheep with good quality wool
Horses with fine features and that can run fast
Whilst not a livestock animal, a good example is an animal that has been selectively bred by humans in many ways to produce breeds with many different characteristics
This is the domestic dog (Canis familiaris), all breeds of which are descended from wolves