The phrase "pure breds" refers to animals, typically dogs or cats, that come from two parents of the same breed. They have a well-documented lineage and their traits and characteristics are consistent within their breed. Full definition
This shaggy tale of a Cinderella story unfolded among the approximately 2,100 pure breds where CC (named for Convention Center) was dumped, but left with a new life and a forever family. (tulsapetsmagazine.com)
The only competition you can not do with a mix breed is Conformation which is for pure breds since it is comparing your dog to the Breed Standard. (straightpoop.com)