An example is the Aberdeen Angus cattle, which have been black for many generations.
With plants, true breeding occurs when plants produce only offspring of the same variety when they self-pollinate. For instance, a plant that has blue flowers will produce only seeds that will grow into plants that have blue flowers. With true breeding, the trait is passed on to all subsequent generations. For this to occur the parents are homozygous for a trait -- which means the parents must be both dominant or both recessive.
See also: inbreeding.