Adapted from The Spontaneous Fulfillment of Desire by Deepak Chopra (Harmony Books, 2003).
The word mantra has two components to it: Man, which is the root sound of the word mind, and tra, which is the root sound of the word instrument. So the word mantra literally means an instrument of the mind.
SIMPLE SOLUTION: The ancient wisdom tradition of Vedanta examined the various sounds produced in nature, the fundamental vibrations of the world around us. According to Vedanta, these sounds are an expression of the infinite or cosmic mind, and provide the basis for every human language. For example, if you sound out all the letters of the alphabet, the vowels and the consonants, you'll hear that these are the same sounds that all babies make spontaneously. These sounds also contain the same vibrations that animals make. And if you listen carefully, you'll notice that these sounds are everywhere in nature. These are the sounds of the wind, of fire crackling, of thunder, of the river rushing by, of ocean waves crashing on the shore. Nature is vibration. The infinite being vibrates, and that vibration is rhythmic, musical, and primordial.
Vibration interacts with vibration. The ancient seers are said to have heard these vibrations of the universe when they were in deep meditation. We can all hear the same vibrations any time. It is very simple. If you quiet your mind and sit silently, you will hear vibrations. If you sit quietly when there is no noise around you, you'll hear a background hum in the air. And if you start paying attention to the background hum, with practice you'll actually end up hearing all the mantras that have been recorded in the Vedic literature.
The Vedas also maintain that if you recite a mantra out loud, its special pattern of vibrations creates its own effects, and can create events in our current physical realm. Reciting the mantra mentally creates a mental vibration, which then becomes more abstract. Ultimately it takes you into the field of pure consciousness or spirit from where the vibration arose. So a mantra is a very good way to transcend and go back to the source of thought, which is pure consciousness. The mantra I use, and that I recommend for achieving synchrodestiny, is the simple mantra "so-hum."
This is the mantra of the breath, if you observe your breathing you'll hear "so-hum" as air moves in and out of your lungs. As you inhale, the sound of that vibration is "so." And as you exhale, the sound becomes "hum."