There are many reasons to meditate, but perhaps the most common are stress relief, personal growth, and spirituality.
Most of us are under a great deal of stress. Between work, bills, school, family, friends, etc., we are constantly busy and have very little time to just relax and unwind. And for many of us, even when we do have an opportunity to relax, our minds and bodies are so used to being in "overdrive" that we find it difficult to really relax until we're completely exhausted at the end of the day.
Meditation offers well documented, long term stress relief. The "overdrive" experience I just mentioned is known scientifically as the sympathetic nervous system response, also sometimes called the "fight or flight" response. It is a natural, healthy, and important response to stressful situations; without it, we wouldn't be able to successfully navigate such difficult situations.
Meditation has been shown to engage the parasympathetic nervous system response: the body's natural counterpart to the sympathetic response. While the sympathetic response readies the body for immediate and decisive action ("fight or flight"), the parasympathetic response is the "rest and digest" mode of the body. The body takes the opportunity to relax and repair itself while no urgent activities are necessary. The mind experiences a sense of calmness and contentment.
Thus, along with such necessities as a healthy diet and regular exercise, meditation forms an important part of today's busy lifestyle.
Some of us can't help philosophizing. We analyze our motives and strive for self-consistency. We gain a sense of meaning when we feel that we are moving forward in our lives, growing into better and more wonderful people. Others prefer to have a simple code to live by and leave it at that. They feel that it is better to spend time living life than to waste time over-analyzing it.
Honestly, I don't think one way is better than the other; I'm sure people at both ends of the spectrum are perfectly capable of leading meaningful lives. While many in the philosophers' camp seem to arrogantly dismiss non-philosophers as being simple-minded, I believe it to be more a matter of temperament. We all find meaning in our own ways.
Personally, I tend to lean pretty heavily towards philosophizing and striving for growth. At the same time, I find that maintaining balance is necessary, and after a certain point, healthy self-analysis becomes unhealthy over-analysis. There is truth to the idea that life needs to be lived rather than simply thought about.
For those of us who strive for growth, there is a vital need for self-awareness. If we wish to truly understand why we believe what we believe — if we hope to even be clear about what we believe in the first place — we need to pay close attention to ourselves. Meditation is all about paying attention. Meditation is paying attention.
For those of us who prefer to live our lives without much self-analysis, there is still a vital need for paying attention. Who hasn't at times felt that life was passing them by, slipping through their fingers? Meditation is an invaluable tool for learning to be present in our lives and appreciate the power and beauty of the moment.
The techniques I teach have no basis in religion or any belief system; as such, they should be compatible with virtually any belief system. I happen to be an atheist. I do, however, believe in living spiritually — in a sense.
There are a range of experiences that I classify as spiritual — although perhaps I am pushing the limits of that word, as I don't resort to the supernatural as a means to explain or justify the importance of these experiences. Looking up at the stars on a clear night in the country, I experience a sense of hugeness, as if I am not limited to my body, but encompass all that I see. Taking a quiet moment to step back and admire the warmth and joy of friends sharing each other's company during a gathering of close friends, I experience a deep sense of connection and belonging. Embracing my girlfriend at the end of a busy day, I relax into an experience of feeling safe and loved.
All of these experiences are ones that I value; I call them "spiritual", although I don't believe in the supernatural. They are the kinds of experiences that are commonly found and increased through the practice of meditation. Whether you are religious or not, whether you consider yourself spiritual or not — if you value these kinds of experiences, you will probably find that you will experience them more and more as you practice meditation.
For those that believe in God or other supernatural matters, they usually find that practicing meditation increases their sense of connection with God and/or the spiritual.