So you want to know what all these certifications really mean????
First and foremost it means simply that the parents of your puppy have been examined by a veterinarian and a veterinary opthamologist and they have been declared healthy for certifications based on the specific organizations specifications...... It does not mean that your puppy will never have problems nor does it meant that my dogs will never have a problem.  As with all of life we are susceptible to our surroundings and as we all age we may or may not have health problems.  It just puts the odds in your favor for good health and a long life. Remember price is once but cost can go on forever if you get a puppy that is not healthy. This way you are setting yourself up for good luck!!

Here is what the foundations say about their certifications. I have linked each foundation so that you can read it here on my website or go directly to their site to see what I am saying....
The Canine Eye Registration Foundation is an organization that was founded by a group of concerned, purebred owner/breeders who recognized that the quality of their dog's lives were being affected by heritable eye disease.  CERF was then established in conjunction with cooperating, board certified, veterinary ophtalmologists, as a means to accomplish the goal of elimination of heritable eye disease in all purebred dogs and now hybrid dogs by forming a centralized, national registry.  This registry is run by the Veterinary Medical DataBases, as a service to breeders and veterinary opthamologists who strive to eliminate eye disease in dogs.  By becoming a member of CERF you affirm your commitment to "man's best friend" by helping to sustain CERF's mission to eliminate heritable eye disease in dogs.
CERF
OFA
Founded and originally incorporated as a private not for profit foundation, OFA was formed in 1966 by John M Olin.  Mr Olin was  a well known inventor, industrialist, philanthropist, conservationist, and sportsman. John Olin was an avid sportsman, hunter, and field trial participant. When hip dysplasia began to impact the performance of Olin’s dogs, he organized an initial meeting with representatives of the veterinary community, the Golden Retriever Club of America, and the German Shepherd Dog Club of America to discuss means of limiting the disease. This ultimately led to the formation and incorporation of the OFA in 1966.  Its initial mission: To provide radiographic evaluation, data management, and genetic counseling for canine hip dysplasia.

While the OFA continues to focus on hip dysplasia, today’s OFA Mission, “To improve the health and well being of companion animals through a reduction in the incidence of genetic disease,” reflects the organization’s expansion into other inherited diseases and other companion animals such as cats.

The OFA is guided by the following four specific objectives:

   * To collate and disseminate information concerning orthopedic and genetic diseases of animals.
   * To advise, encourage and establish control programs to lower the incidence of orthopedic and genetic diseases.
   * To encourage and finance research in orthopedic and genetic disease in animals.
   * To receive funds and make grants to carry out these objectives.


The OFA Databases:

The OFA databases are core to the organization’s objective of establishing control programs to lower the incidence of inherited disease.  Responsible breeders have an inherent responsibility to breed healthy dogs.  The OFA databases serve all breeds of dogs and cats, and provide breeders a means to respond to the challenge of improving the genetic health of their breed through better breeding practices.  The testing methodology and the criteria for evaluating the test results for each database were independently established by veterinary scientists from their respective specialty areas, and the standards used are generally accepted throughout the world.