The meaning is ongoing repentance (Have mercy on me, a sinner) and a perpetual directing of our focus on our Savior (Lord Jesus Christ, Son of God) and a calling on Him for help.
If the purpose is to focus on the meaning of the words, it's not to empty the mind (the way Budhists and Hindus do.)
That means there is a right and wrong way of doing it (which is what I was asking.)
The purpose is not
to focus on the meaning of the words, as in think or ruminate about them. Please take the time to read Bishop Kallistos' article, which I linked to in my first response. Pages 85-87 in linked book address your questions quite directly, I think. Pages 81-85 address the theological and scriptural basis of the Jesus Prayer.
Here's the intro to the article:
"‘When you pray,’ it has been wisely said by an Orthodox writer in Finland, ‘you yourself must be silent. . . . You yourself must be silent; let the prayer speak.’ To achieve silence: this is of all things the hardest and the most decisive in the art of prayer. Silence is not merely negative — a pause between words, a temporary cessation of speech — but, properly understood, it is highly positive: an attitude of attentive alertness, of vigilance, and above all of listening. The hesychast, the person who has attained hesychia, inner stillness or silence, is par excellence the one who listens. He listens to the voice of prayer in his own heart, and he understands that this voice is not his own but that of Another speaking within him." http://www.orthodoxprayer.org/Articles_files/Ware-1%20Prayer%20and%20Silence.html