here is the ACA's website:
ACA American Canine Association
The ACA is one of those registries that came up as competition for the AKC. They are basically a registry for pet breeders. They are a little cheaper than the AKC and they don't require as much proof of pedigree to register a dog. It's not the the other registries are "bad" just that they are easier to abuse by dishonest breeders and puppy mills.
They also don't participate in things like health research, shows, etc t(though they do occasionally sponsor shows, it's NOTHING like an AKC show).
Being ACA registered doesn't mean your dog isn't pure-bred. It just means your dog is registered with the ACA. And, being registered with the AKC isn't really "proof" that the dog is pure-bred either. Both registries rely on information from the breeder. But, the AKC at least provides for DNA testing of sires and dams and does occasionally verify the parentage of puppies using that DNA.
If you want, you can take your pedigree from the ACA and provide it to the AKC to see if your dog can be registered with the AKC.