What are Shin Splints?
Shin splints is a general term to describe pain in the lower leg. This can range from anything from tendinitis, stress fractures, muscle strains or compartment syndrome. Typically when athletes refer to "shin splints" they are talking about pain along the medial (inside) part of the bone in the lower leg (tibia) especially during and after running. The medical term for this condition is Medial Tibial Stress Syndrome.
Medial Tibial Stress Syndrome (MTSS) is caused by repetitive micro-trauma. This is common in running sports such as basketball, running, soccer, and gymnastics. This problem is usually the result of lower leg muscle weakness, shoes with little support/cushioning and over training. Improper striking of the foot can also lead to this condition.
MTSS usually starts as only causing pain after activity. Then it will cause pain before activity, while warming up, and after activity. It then will cause pain before, during, and after activity. Finally it will cause pain during that is debilitating enough for the athlete to not be able to do activity.
Typically the pain associated with MTSS is a result of the posterior lower leg muscles "pulling" on the bone. The outer layer of the bone is highly innervated with nerves so is very sensitive to this pulling. Excessive tightness in these muscles will result in more irritation of the bone and more pain. Ruling out a stress fracture is important, however sometimes the stress fracture will not show up on Xrays and either a bone scan or MRI is needed to see the stress fracture. 
There is a difference between a stress fracture and a stress reaction as well. A stress reaction is the result of the bone breaking down more than it is rebuilding itself. This will show up as a "hot spot" on an MRI or bone scan but there is not a crack in the bone. When the condition has progressed to the level of a stress fracture, there is a definitive crack in the bone with an MRI or bone scan.
Treatment and Management
Rest is crucial. Rest allows the bone and muscles time to heal and rebuild from the repetitive micro-trauma. Being able to cross-train by supplementing running with biking, elliptical or water workouts is a great way to maintain cardiovascular fitness. Strengthening the lower leg and foot will help with shock absorption and overuse problems associated with the weakness of these areas. Stretching out the calf and the Achilles tendon will also allow for good shock absorption and allow a normal/proper gait and will take unneeded stress off improper areas.