The name of this certificate, Pedigree, is very well known but what it actually is, what it is used for and why you need to ask for it, is definitely less known.
Meanwhile, it is the ONLY document that can ensure that a cat is purebred. It can be argued that there may be children of pedigreed cats, and therefore purebred cats, which do not have the pedigree and consequently would also be purebred. In fact, this is not the case. If the child of two purebred cats does not have a pedigree there will be a reason , so you cannot be 100% sure that it is purebred and it cannot be sold as a purebred animal under Italian law. 
The Pedigree (technically the Genealogical Certificate) is the identity card of the cat (ditto for the dog) and establishes that the cat is raised according to the rules. While he is the son of two parents both with pedigrees, who are regularly subjected to checks necessary for the breed, that the breeder carries out his activity in compliance with the rules on animal welfare, that he undergoes checks, knows what he must do before during and after delivering a puppy.
Then that the birth report has been duly registered and that the necessary acts have been followed for the registration of the puppy in the so-called "Book of Origins", which is a register, more modernly speaking a Data Base, which collects all the data of all pedigreed cats and their family ties.
These are the basic definitions, which still do not explain why it is essential to ask before buying a purebred cat.
So let's reverse the conversation: who does NOT have the pedigree? And more precisely, who do they not give it to? Because? If it is true that the typical proposal is € 1,000 with pedigree, € 500 without, and if it is true that the cost of a pedigree ranges from € 10 to a maximum of € 26, it does not seem that something very doubtful has not been there. said?
And also: one could sell the puppies for a thousand euros   and in order not to spend € 20 give up 480 € of earnings?
Come on!
Relying on the fact that the typical buyer is in no way in a position to verify the validity of a pedigree , anyone can show you a cat (this is the mother!) And tell you that it has the pedigree, and can even show it to you (paper , not watermark). But are you able to tell if it is authentic? If it belongs to that cat there?  if it is "ministerial"? Or are they homemade? What happens most frequently is that a breeder, no matter if simple private or amateur or professional, can make a cat too many kittens (more than 3 pregnancies in 24 months is against the rules) so he does not report the litter for not having penalties. . By accepting a puppy without a pedigree, we finance the activity of one who exploits the cats by making them give birth too often, regardless of the health and well-being of that mother.
Or it happens that someone buys a "pet" cat, where in the contract it is expressly written that that cat must not reproduce. Without worrying about the reasons for that ban, the improvised breeder makes the cat reproduce but cannot ask for the pedigree because otherwise he would declare himself. Apart from the fact that incorrectness is never an isolated case, and if one is incorrect it is always and with everyone, even with you . But what if that prohibition of reproduction was due to hereditary or genetic defects? We have news of kittens operated on for cataracts at 6 months, a hereditary problem that is solved by sterilizing cats with that defect, so even those who are born healthy and do not develop the disease must be neutered. But someone is not interested in the suffering of a kitten who at 6 months has to undergo eye surgery ...
The saddest cases are those of those who regret having bought a cat without a pedigree and mate it with another "similar" breed cat and then tell that they are both pedigreed or that the parents were purebred, and since none the DNA test will mail… here it is the purebred cat without pedigree.
All of the above are nothing more than scams , which feed on superficial considerations such as "only serves if you want to compete" or "only serves if you have to reproduce". The truth is that the pedigree serves to know what the needs of the cat we have purchased are, because each breed has its needs and we will be better life companions for our cats if we are sure we have correct information on their genetic makeup, not only for lethal diseases but for everything that is typical of that genetic line, from food intolerances and allergies, from the problems of aging to character. 
We know many things about the purebred cat, about its needs and needs. If it is purebred, genetic tests can guide us towards prevention, otherwise not. If we know exactly parents, grandparents and siblings we can monitor genetic and hereditary diseases, support research and science. If we "cheat" on pedigrees we damage research and science ... And I could go on for hours.