A japa mantra is a word or hymn that bears a spiritual significance; usually, the name of the Almighty or words to praise God. From Sanskrit, japa means "to repeat quietly" and mantra means "instrument of thought."
Japa is the way of chanting or muttering the particular word or hymn repetitively, but, at the same time, so subtly that only the reciter can hear it and nobody else. In fact, according to yogic discipline, to attain the desired spiritual outcome, a practitioner needs to chant the japa mantra internally (in his/her own mind). Reciting the mantra internally may not come easily for beginners; but, through slow and steady effort, a practitioner will be able to do the mental recitation within a few weeks. (Get started with your japa chanting with Our 4 Favorite Chants.)
One or Many Syllables
A japa mantra can be of two types: monosyllabic (i.e. Om or Aum) or a phrase of words (i.e. Om namah Shivaya). According to Hatha yoga, Shabda Brahman, or the "Supreme Sound," is the ultimate source of all kinds of sound happening in and around the universe, whether audible or inaudible. But, while each and every sound possesses some great force, no sound is more powerful than a japa mantra. For thousands of years, Vedic people have drawn words from different Vedic and non-Vedic sources, putting the practice to various uses, but the most significant is communicating with the Almighty.
Mala Beads Optional
Another familiar way of performing japa mantra is with japa mala, or a string of 108 prayer beads. With the mala, the practitioner must recite the entire mantra once for every bead, counting to 108 for a full circle. Wondering why 108? Well, Hinduism considers 108 a pious number. (Learn more in Meditating With Mala Beads.)
On a broader perspective, soulful mental recitation of a japa mantra can result in ultimate salvation or the ultimate spiritual freedom. A sacred hymn works the best if it is given by a guru or other spiritual teacher to a disciple through the process of initiation. (But you don't have to wait until you find your guru, find out "What's My Mantra?" next!)