A dog's pedigree is a list of it's parents, grandparents, great-grand parents etc, their titles and colors. A breeder will pay a great deal of attention to the pedigree of any dog that is being considered for breeding.
A pedigree is read left to right. The first two dogs listed are the parents. The male or "sire" is always on the top, the female or "dam" is listed on the bottom. The next generation listed to the right are grandparents. An example is shown below.