(an x-ray of normal hips, from Wikipedia Commons)
A dog may not receive an OFA rating prior to two years of age, which is one reason it is believed that a reputable breeder won't use a dog to produce before that time. Hip dysplasia, in short, is a misalignment of the bones of the hip. It might affect one hip, or both, and though there are surgeries and treatments that can be enacted in order to help a dog out, if a dog and bitch have low scores through OFA or Penn Hip, they should not be bred, because they will pass those hips on to their puppies.
(depiction of hip joint structures in hip dysplasia, from Wikipedia Commons)
Elbow dysplasia involves a misalignment of the radius and ulna in the joint, and separations and fractures in the elbow joint.
1 step between articular surfaces of radius and ulna, 2 isolated anconeal process, 3 fragmented medial coronoid process (FCP), OCD of the medial condyle
(Manifestations of elbow dysplasia in dogs, from Wikipedia Commons)
Things other than genetics can affect dysplasia in dogs. One of these things is inappropriate exercise during the formation of bones; for instance, you don't want to bike with your puppy. Joints are forming, growth plates are still open, and that kind of forced exercise can cause a lot of damage. Additionally, it's more than worthwhile to keep your dog an appropriate weight. Just as extra weight on a human can cause health problems, it has similar ramifications in a dog, and their joints suffer for it.
There are a number of operations to treat hip dysplasia, ranging from trimming the rim of the joint (shudder) to removing the head of the femur, to a total hip replacement. The different procedures are recommended based on the size and weight of the dog. It seems that elbow dysplasia treatments also involve at least one type of surgery (scraping defective cartilage and removing fragments), and also medical options to reduce inflammation. None of these options sound pleasant, you might notice. http://pets.webmd.com/dogs/ is a great informational site, and where I cribbed the operational information from for the purposes of this post.
We want our dogs to have happy and healthy lives. If you decide to go with a breeder, try to make the best choice possible, and choose a breeder who fully health tests his or her dogs. That way, you're giving your prospective family member the best shot at living long and living well.