This article by Rick Hanson, author of Buddha's Brain, offers a great summary of the neurological benefits of meditation:
Meditation is to the mind what aerobic exercise is to the body. Like exercise, there are many good ways to do it and you can find the one that suits you best.Lots more detail about what mindfulness meditation does for the insula, hippocampus, and PFC on the link.
Studies have shown that regular meditation promotes mindfulness (sustained observing awareness), whose benefits include decreased stress-related cortisol, insomnia, symptoms of autoimmune illnesses, PMS, asthma, falling back into depression, general emotional distress, anxiety, and panic, and increased immune system factors, control of blood sugar in type 2 diabetes, detachment from reactions, self-understanding, and general well-being.
And here's a Ted talk about how meditation affects your heart, brain, and creativity.