The phrase is difficult to render into English, because each word or set of words contains many alternative meanings. One translation, used by Nichiren Shu, is "Adoration to the Scripture of the Lotus of the Perfect Truth", but without an understanding of the symbology behind those words, the meaning is lost.
On one level, this mantra is the title of the Lotus Sutra, held to be the Buddha Shakyamuni's penultimate teaching. On a different level, it is a distillation of the entire sutra, i.e., all the sutra's teachings are summarized in the title. Third, this mantra is the Ultimate Law permeating the universe.
It can also be translated as Namu (devotion), the act of practicing Buddhism; Myoho (Mystic Law), the universe and all its manifestations; Renge (the lotus flower, which blooms and seeds at the same time), representing the simultaneity of cause-and-effect; Kyo (sutra), a teaching, specifically, the teaching of the Buddha Shakyamuni. Thus, a loose translation of Namu-Myoho-Renge-Kyo may be, "Devotion to the teaching of the mystic law of the universe."