Knowledge of pedigrees is often underrated. For most beginning breeders it takes a while before they realize how important this is, and they learn later on what they have to look for in a pedigree.
Often we see that the animal we bought first, later on does not meet our expectations anymore with regards to e.g. the pedigree. In the years after we buy our first breeding cat we gain more insight about the family background of our breeding cat. It happens more then once that we are not entirely happy with what we learned. For instance because the ancestors of our cat have been used very often, and it is difficult to find a supplementing partner to our breeding cat. Or because we later find out that one of the ancestors has passed on bad traits to some of its offspring, like genetic defects or weaknesses with relation to the breed standard.
A lot of people do not know what to look for when they see a pedigree. The fact that a cat has a pedigree does not always mean that the cat is a purebred animal. In some breeds crossbreeding is allowed. For some other breeds the studbooks are still open and cats without a pedigree but who share a large resemblance to the breed can be used for outcrosses. In both cases this is being done to widen the gene pool. There are strict rules drawn up for these outcrosses, that describe which cats are, and which cats are not allowed to be used as outcrosses in a certain breed.
However, in the past there have been some undesirable crossbreeds, that up to this day still cause problems in some breeds. Like the forbidden point gene (Siamese color) in the Maine Coon breed.
How can you tell if your cat's pedigree is all right? Some European cat associations note on the pedigree the EMS code of each cat. For a Norwegian Forest Cat, this is "NFO", for a Sacred Birman this is "SBI" and for a Maine Coon it is "MCO". If the description on the pedigree says "XSH" or "XLH", this means that the cat is not a purebred cat. (XSH stands for domesticated shorthair, XLH stands for domesticated longhair.) You can also find descriptions like "exp. 1e generation" or something like that on the pedigree. (Where "exp." stands for experimental.) Again, this means you are dealing with an animal that is not a purebred.
Even if you do not know what all the signs, codes and abbreviations on a pedigree mean, you will still be able to see if everything is ok, you just have to think logically and pay attention. If all but 1 or 2 animals have the same abbreviations, ask for explanations. Contact other breeders, or the association that made the pedigree. They can explain to you what the abbreviations mean, and why these 1 or 2 cats have different descriptions. Never assume that a pedigree stands for quality or integrity, both for the breeder as well as for the cat. Investigate things yourself, and sift to the bottom, for as many generations as possible. A pedigree is not a warranty!
Finally, there are other things you can derive from your cat's pedigree, like the inbreeding percentage. To calculate the inbreeding percentage as good as possible, it is very important to look beyond the 4 or 5 generations that are listed on the pedigree. If you see the name of one cat mentioned more then once, it will not take you long to realize some form of inbreeding took place. The level of inbreeding can be calculated by a pedigree program like PawPeds.