There are a number of aspects to this question. Perhaps the one most applicable is the teaching of the fathers on the different "kinds" of prayer. In the Art of Prayer St. Theophan the Recluse (a Bishop in nineteenth century Russia) reiterates the teaching of earlier fathers concerning 3 kinds of prayer - 1. prayer with the lips, 2. prayer with the mind, and 3. prayer from the heart.
1. Prayer with the lips is simply the physical repetition of the words of the prayer. This by itself is empty. If we mindlessly repeat the words of prayer or if we just mindlessly "babble" spontaneous words, then this is not true prayer and not pleasing to God. Prayer of this nature has at best no effect on the soul, however, it is more likely damaging to the soul because he who prays this way deceives himself and thinks that he is praying.
2. Prayer with the mind is the second "stage" of prayer and is (and should be) coupled with prayer of the lips. Whenever we say a prayer, whether mentally or verbally, the mind should be wholly involved in the prayer. This is what the fathers call "attention" in prayer. It is the mind's involvement in concentrating on and attending to the words of the prayer. Prayer with the mind gives understanding and meaning to the prayer of the lips and these two together form most often the type of prayer that we offer to God and is beneficial but not yet perfect.
3. Prayer from the heart. Bodily prayer (as represented by prayer of the lips, but not limited to verbal expressions - making the sign of the cross for example) and mental prayer lack yet one element, and that is the heart. The heart, according to the teaching of the fathers is the seat of the soul and of all feelings and as such, must be involved in any prayer that we make. Just saying the words (lips) and understanding them (mind) is not enough - we also must mean them (heart). We are created with a dual nature, body and soul. The mind is the "lowest" part of the soul and the heart/spirit is the highest Perfect prayer must come from and involve our whole being - body, mind and heart. What the fathers refer to additionally as "prayer of the heart" is not this third type or stage of prayer, which is within our ability as creatures to offer to God by our own strength but rather it is a gift from God transforming our souls so that the heart continually prays to God not prompted by bodily or mental activity and thereby infuses the mind and body with prayer .
Part of the teaching of the Church about vain repetition in prayer is that the empty prayer such as mindless repetition or babbling of words should be avoided and is of no effect. And Jesus equates the prayers of the pagans with this "empty", "wordy" type of prayer. Notice how He does teach us to pray immediately after this instruction of how not to pray - "Our Father... ". Just the first words evoke the deepest, most personal of all natural feelings of the heart,- those of a child toward their parent, thereby immediately drawing not only the lips and the mind, but the heart as well into the prayer.
Now to shift perspective a little, I'd like to add to your wife's question, my own observation of what heterodox, especially Protestant, Christians "object" to when they use this scripture as a criticism of Orthodox Christianity (as well as Roman Catholicism, Anglicanism or other liturgically based traditions) . The most often cited "offending" prayer in this category is "Lord have mercy" which we seem to say over and over and over again. But (assuming this prayer is said with attention and feeling) is there any other prayer we could say? What else can we ask for from God except mercy. We certainly deserve nothing from God and so we ask for His mercy. We can't presume to know better than He what is most spiritually beneficial for anyone, not ourselves, not others and so we commit our prayers for others to the words, "Lord have mercy" knowing that by doing so we ask that God decide, in His mercy, what is to be done or provided in any given circumstance and then act according to what is needful for the salvation of each and every person for whom we pray. While the words of the prayer "Lord have mercy" are the same, the context and meaning and intent of the words is never the same. "Lord have mercy" is the universal prayer, it is applicable to any and every situation and it is the prayer we pray when we don't know how to pray.
When you consider only the words of our prayers, they remain generally the same, but that is only prayer with the lips. It is the prayer with the mind and heart that activate and enliven and give meaning to the words. If we pray for "the peace of the world" that can mean many things and we fill that petition with our intent and then ask not for this or that resolution to a particular conflict, but rather for God to act in His mercy, according to His perspective and knowledge and understanding of what is best for the salvation of the world and the establishment of the Kingdom of peace. If we pray for "those who are in captivity" again the words stay the same but the meaning can shift widely from who is in captivity to what we mean by captivity and again our request is not this or that specific resolution, but that God, who is all knowing and all seeing and is aware what the needs of each soul are, will act in this situation according to His mercy.
The teaching and experience of the Church about prayer is like a vast and deep ocean and we have described only a little shallow section of beach! To know more, one must experience the prayer of the church, in the context of all of the christian faith and it's practices.
Fr. David Moser - St Seraphim Orthodox Church, Boise, Idaho
We confidently recommend our web service provider, Orthodox Internet Services: excellent personal customer service, a fast and reliable server, excellent spam filtering, and an easy to use comprehensive control panel.