O.F.A. stands for Orthopedic Foundation for Animals, and they are a canine health registry and data bank. They are based in Columbia, MO. In Labradors, reputable breeders will x-ray hips and elbows on all their breeding stock to verify that they are free from hereditary disease. This is done prior to breeding them. Breeders will then send those x-rays to the O.F.A. for their professional evaluation, as well. Board certified radiologists study the x-rays and issue an evaluation based upon their collective opinions.
The OFA data base now includes many more types of clearances besides hip and elbow readings. You can also do pedigree research to see health status of parents, siblings and half-siblings. It is both a great breeding tool and also a wealth of information for pet owner's.
For more information on this organization, please look at their web site at www.OFFA.org.