I first became familiar with this mantra in Northern India, almost a decade ago, often hearing it repeated quietly as the Tibetans went about their daily tasks. As I've looked into translations, I have found many! It is a mantra for the bodhisattva of compassion, Avalokiteshvara.... also referred to as Chenrezig in Tibetan Buddhism.
Although one simple English translation of the mantra is: "Hail to the jewel in the lotus flower!" there is still lots of room for interpretation as to what that means. One suggestion I came across was that the jewel is compassion and rests inside the lotus, which is wisdom, thus signifying that compassion is an integral part of wisdom and of equal importance. A friend and Tibetan translator offered to me that it's believed that simply hearing this mantra has the power to protect one from rebirth in the lower realms. She also shared that there are six syllables in this mantra, each of the syllables are connected with the beings of each of the six realms. So as one recites the mantra while giving rise to great compassion for all beings, one purifies the karmic imprints and suffering of the six realms of samsara, for oneself and all sentient beings.
Using "Mani" at the beginning of the chant is certainly not traditional, but is how I learned the song, and I've kept it as such. Sometimes when I sing this song, I remember the depth of compassion and forgiveness I found not only in the Dalai Lama himself but in so many of the Tibetans I met on my travels. May I always remember the value and wisdom of compassion, om mani padme hum.