It stands for United Kennel Club the are a good registery for breeds that the AKC doesn't register (such as APBT), but be careful because some breeders will use UKC registration to get around dogs sold to them on AKC limited registration. AKC limited registration is a way for a breeder to sell puppies that do not meet breed standards and prevent any puppies that dog may produce from being registered. Some unscrupulus breeders will register there dogs with the UKC to get around this so they can register the puppies. So if the breed is also AKC registerable ask why they are using the UKC. Also ask for information on the parents there breeding dogs such as there registration numbers and if they were AKC or UKC. If there dogs parents were AKC that is a warning flag.
UKC is the United Kennel Club. I have friends who have dogs double registered with UKC and AKC. She is doing conformation first in UKC and then, with that experience, goes on to AKC. It's not a bad registry, but I would favor a dog that is dual registered myself.