If you have a scientific inclination, then these guys seem to be doing a good job of explaining the neuroscience behind meditation. Although it seems to me that neurology is still quite a basic medical science, but they seem to know that too.
You might also be interested in Richard Davidson who put some monks into an MRI machine and derived some interesting results. He's also affiliated with the Center for investigating healthy minds.
Here is my take on things:
What is meditation?
Put simply, meditation is training the mind to see experience as it really is. It is a fundamental looking into ourselves.
In practical terms, there are numerous meditation techniques but there are essentially two main methods of meditation - mindfulness ( leading to vipassana) and samadhi (concentration). Mindfulness is cultivating awareness and samadhi is cultivating tranquility, although you can't really do one without the other. The goal of each technique is to generate a steadiness of mind from which phenomena can be observed. Mindfulness leads to momentary concentration, while samadhi leads to access and then absorption concentration. In both cases the mind becomes calm, steady and focused - this altered mind state is a primary source of interest because our everyday mind is now longer running the show.At this point, we can now be said to be meditating rather than attempting to meditate.
Meditation techniques were developed over 2000 years ago when there was no science as we would know it today. However, ancient meditators discovered that meditation led to many different insights - namely that it is possible to transcend the limited self view, that it is possible to be free, and that the mind can be released. Neuroscience, then, is attempting to describe these different insights in the modern scientfic way - this chemical leads to this mental state, these brainwaves lead to this state of consciousness.
Answering the big question
The big question is "who am I?" Neurology wants to know scientifically and we want to know because that's the way we are. Experienced meditators know that there is no real answer because it is a loaded question. This is why we get answers like "I am thus" from ancient times. Perhaps the real question is "how do we work?" and hopefully neuroscience will help explain this so we can derive social and health benefits from it in the future. Perhaps we will learn to transcend some of our more primitive impulses.
Trends in neuroscience
There's a lot of interest in the impact of meditative techniques on the mind. Studies have shown that the brain can be altered by using meditation for as little as two weeks. This ability for the brain to be altered by experience is known as neuroplasticity. There's also interest in how the mind influences the health of the body - do people who meditate heal more quickly? Does the way we think influence our genes? - epigenetics might come up with some answers to this. There's certainly a lot of exciting things to look forward to as mainstream science uncovers more and more benefits from the wonder of meditation.