The term shin splints is used to describe a certain kind of injury, usually encountered among runners. Shin splints are a painful inflammation of the lining of the muscle on the front of the lower leg (the shin). This can sometimes extend to irritation of the bone and muscle. It is often caused by running on hard surfaces (concrete or asphalt), lack of strength in the effected area, or genetic predisposition (can be attributed to bone structure, muscle strength etc.).
In addition to the treatments mentioned in the other write-up, many people swear by orthotics (a hard plastic, supportive shoe insert) which, though quite expensive, can counter some problems with leg structure. Orthotics are usually made by orthopedists or physical therapists specializing in orthopedic problems.
A common preventative measure is achieving strengthening of the general area by writting the alphabet on the floor with the big toe every chance you get. This improves strength throughout the ankle and lower leg though it won't help much after the onset of shin splints.
It is important to note that shin splints are different from stress fractures of the tibia. Shin splints can be safely, though certainly not painlessly, ignored when necessary. Stress fractures cannot and should not be ignored as they will progress into serious problems.