Really, it's not religious. It is merely the momentary pause of thought. It is as religious as the holding of breath as you dive under water, or the halt of stepping as you pause from a rapid pace. It's as religious as the not eating that sometimes happens between meals. It's as religious as summer vacation, the space between words, or briefly being between jobs.
Meditation is innately human, and certainly in simpler times gone by, meditation came easily to us. Sitting under a tree near the river, listening to the sound of water moving, I suppose thought naturally paused for a few minutes in peaceful, spontaneous harmony. Or while watching the magnificence of the stars emerging in the sky as the world grew dark and quiet, rest undoubtedly came naturally to the mind. Science now tells us that this kind of rest for the mind is healing to the body, and it also helps to rebuild brain tissue and prevent several psychological disorders, including Alzheimer's and ADD.
Obviously, no one person, religion, or organization can own inner peace. It is a human experience, a state of being that every individual can access within themselves. So if we can access inner peace within ourselves, that makes inner peace ours, doesn't it? The word, "meditation", merely describes the act of accessing the inner peace which is already inside of you. You own it. Therefore, meditation belongs to whomever chooses to access their pre-owned inner peace. Your meditation and inner peace are exclusive possessions of yours. And however you access your inner peace is meditation, whether it is a quiet stroll, sitting in lotus position humming, or climbing a large rock.
And just as religion cannot claim exclusivity to food, sleep or play, neither can it claim meditation. On the other hand, you could make eating a sandwich religious with a great deal of effort and organization. But a sandwich is still just a sandwich, and meditation is still merely the momentary pause of thought, brought about consciously.
Of course, meditation has been a part of every religion as long as history can record. I attribute meditation's popularity in religion to it's effect: it makes us feel better. Powerful, nourishing, and healing, food and meditation have a lot in common, whether or not they're connected to a religious belief system. Food is just food, but when it's included in religion, it takes on holy significance. The same is true of meditation. "Meditate in your heart, and be still." Psalm 1:2.
It is worthwhile to mention that repetition has been studied extensively, especially by Herbert Benson at Harvard, where they've found that it can lead to deep meditations and peaceful states of being which they call, "The Relaxation Response." What's interesting about these studies is that they've found it doesn't matter what you repeat, whether it is Hail Mary's, Sankrit mantras, or your mother's maiden name. It is the repetition for at least 20 minutes that leads to pronounced responses of peace in the body and mind. So if you enjoy religion, you can try saying a prayer that you connect with, and use a rosary, subhah, tzitzit, mala or kitchen timer to keep track of 20 minutes for you. At the end of your repetition, you may have more success pausing your thoughts than otherwise.
If you are not religious, you needn't fear that you'll become religious if you choose to meditate. You will, however, prevent mental illness and rebuild brain tissue. Also, meditation has been linked to the prevention of stress related diseases, which make up a large portion of all diseases. Meditation empowers the meditator with health and clarity. You just have to stop thinking at will.