What is Meditation? Meditation is the practice of turning your attention inward. It is very often these days called “Mindfulness”. On a very basic level it is mental releasing the mundane concerns of the day and turning your attention to the deeper levels of your mind. Often attained by simple visualization techniques to take you to a quiet place where you can “hear” your inner voice, spirit guides, and Greater Self and/or access memories and information provided by any of these sources.
There are many ideas as to what you hear there, I am inclined to believe they are all probable, and like everything else in the spiritual realm, is completely dependent on your personal path.
How is it Done? Create an environment that is conducive to peace. Try to avoid distractions, use incense, music, lighting, your clothing, everything you feel will help you to manifest a special, relaxing space. Meditation starts with breathing exercises. Slow, deep breaths that you are aware you are doing. Awareness of your breathing pattern is the first major step. Then you begin the visualization, chanting, or whatever method you find works for you to slowly travel inward, allowing the chatter of the surface thoughts to just drift by like birds that are flying by and away. Once you achieve the inner stillness (which is mindful but not empty) you will find a clarity and point of view that steps back and observes. When done, you simply follow the pattern in reverse and finish with some more conscious breathing to re-enter the world around you gently.
What are the Benefits? Meditation like any exercise, mental or physical, gives the most profound results when practiced regularly. Just as one or two sets of crunches will not give you a healthy body, meditation improves with daily practice. The more often you meditate the deeper your results. Meditation will give greater clarity of thought over-all. It will help you to regulate and channel your impulses. It will aid in problem solving, and the ability to release what you cannot control. These are definite results you can expect. Reports of improved physical well-being, better sleep patterns, improvements in ailments and chronic physical complaints. Also practitioners have also found the they become more aware of their own mental processes and therefore have a greater ability to consciously change undesirable patterns. Many report greater recall of dreams and awareness of Astral activity. Deeper and more sustained meditation can bring spiritual growth and awareness and even trigger spiritual awakenings.

Here is the Science:
From sleep to awake and alert, the brain goes through 4 stages measured in waves: delta, theta, alpha, and beta. Research has linked the lower frequency alpha and theta waves to meditation. Alpha waves are decreased and theta waves increased, leading to a state that is more relaxed while maintaining a sharp awareness. Other studies indicate a voluntary heightened control over attention while meditating as well as a greater sensitivity to emotional expression and positive emotions.
Long-term benefits of meditation effect eight specific areas of the brain which include those areas responsible for meta-awareness, extero-receptive and intero-receptive body awareness, memory consolidation and reconsolidation, self and emotion regulation, and intra- and inter-hemispheric brain communication. Also, meditation plays a role in protecting grey matter against natural reduction. Further study shows a higher tolerance for pain.
A number of studies have linked meditation practice to differences in cortical thickness or density of gray matter. One of the most well-known studies to demonstrate this was led by Sara Lazar, from Harvard University, in 2000. Richard Davidson, a neuroscientist at the University of Wisconsin, has led experiments in cooperation with the Dalai Lama on effects of meditation on the brain. His results suggest that long-term, or short-term practice of meditation results in different levels of activity in brain regions associated with such qualities as attention, anxiety, depression, fear, anger, the ability of the body to heal itself, and so on. These functional changes may be caused by changes in the physical structure of the brain.