A kennel club is usually a gathering of dog breeders, discussing things relevant for breeding of dogs. They became popular in the mid 1800s. They keep up breed standards (what they think the breed should be similar to) and make the rules for dog shows, and occasionally training programs (where the dog is trained to do a certain thing).
There are a large selection of types of kennel clubs. They can be "all-breed clubs", (where there are a list of dogs they have decided to recognize), or a breed club which simply handles one breed.
Sometimes, a kennel club is only concerned with one race of dogs.