Om, Mani, Padma, Hum

Is one of the most ancient mantras (thinking tools) known. It's purpose is to assist the mind in perceiving the process of life and the underlying control networks of becoming. All becoming.
For those familiar with fractals, a mantra is like a fractal seed and a fractal formula combined.
With iteration of the mantra, a pattern begins to form in the pixels of our mind becoming more interesting, colorful and resolved with each iteration.
Unlike the far out, but imaginary visions produced of most fractals, the pattern created by this mantra has an immediate, obvious, and powerful meaning. It is what we are, why we are, how we are, and knowing we are. In that order.
As with all mantras, each word in the phrase is a mental cue, a focus, for a complex, holistic concept.
Think the word, flood your mind at the same time with the concept, complete with all the shades and colors of emotion and knowledge you can bring to focus on it.
As you learn more about each concept, you add to the texture, the relief, the depth and duration of the experience. It is like saying the name of a loved one and letting yourself be instantly aware of all that you know about your loved one, complete and whole and full of life. The greater your knowledge and your love, the more profound the impact of the name.
Om, Mani, Padma, Hum is a complex mantra. A spiral progression of concepts. The basic progression of existence, the mantra applies to every living being, to thoughts, to language, even to suns and galaxies.
" The more you know about each word, the deeper the impact of your thinking or saying the word.
" The more you know about the relationship between the words, the more universal and powerful the mantra becomes.
You can mess it up, too. Easily. Just saying the words is meaningless. Despite what some people think, saying Om or chanting it or singing it has no "power" at all. It is true, however, that the sound itself amplifies the Mantric power of the word. It has an actual physiological effect on the human nervous system. But it only becomes a mantra if the tool is used. A hammer is just a hunk of metal attached to a bit of dead tree unless someone picks it up and uses it to hammer something. However a hammer can also have meaning without being used, providing the people involved know what it is, where it is, and what it can do. The power behind the mantra is the same power behind the hammer.
So what are the concepts associated with this ancient and powerful mantra? There is an excellent book about this, Foundations of Tibetan Mysticism listed in the references. A good scholorly bit of work, if a bit heavy on the ancient analogies. In a nutshell, however, here is what you are supposed to focus on when saying or thinking the mantra.