The AKC is the American Kennel Club. It has tracked the registrations of dogs in the USA for a very long time. Having a dog registered with the AKC does not mean anything as far as health or temperment, just whether the dog is bred from two dogs of the same breed. There is also a slight chance that a dishonest breeder could fake these records. The AKC though is very concerned about that and has doubled and tripled it's checks making sure that breeders stay honest about whether they are breeding purebred dogs to each other and exactly who the sire and dam are of the puppies are.
As soon as the AKC started these major checks to determine that people are being honest about who they are breeding, including DNA tests on multi-used sires, many of the dishonest or large facility/careless breeders found that litters of theirs were being rejected by the AKC as not bred by the dogs they said they were bred by.....so the ACA, ConKC, and many other easy registries were born. These registries are based on the idea that their breeders don't lie, that all dogs they say are purebred are, no proof necessary. If someone says their litter of puppies are beagles, they register them as beagle, even if they're 100 lbs or covered in bushels of fur.
The AKC is not a guarantee of anything, but that the puppies are the right breed to the best of their knowledge and they try very very hard to make sure of it.
The ACA means even less. In fact it means nothing at all.