In praying, do not babble like the pagans,
who think that they will be heard because of their many words.
Prayer is not an incantation or a secret code that causes things to happen. Pagans tended to approach prayer as if a sufficient recitation of divine names and other formulae would automatically achieve their desired results. They had no thought of being in relationship with these deities to whom they prayed. Their actions stemmed from their belief that their gods didn't really care about them, that they needed to be made aware of their petitions, and more or less forced into acting on them. It wasn't their perseverance in prayer that Jesus criticized so much as the motives for it, and the image of divinity that caused them to feel it was necessary. It was redolent of human desperation combined with a lack of hope.
Do not be like them.
Your Father knows what you need before you ask him.
In order to avoid praying like the Pagans, Christians would need to appreciate the difference of the Father from all of those false gods. He did not need to be made aware of the needs of his people. He knew them. He did not need to be forced into action. He himself desired their good more than they did themselves.
Our Father who art in heaven
When praying, Christians were to first remember the relationship that made their prayer possible. God had chosen to adopt a people as his own children, allowing them to share in that which was naturally proper only to Jesus Christ. And that image of fatherhood was meant to inspire absolute confidence in his goodness and providential care. It was true that many Christians would have even in those early years have experienced brokenness in earthly family life, now so common, that made the concept of God as Father harder to appreciate. But God was a Father with none of the limitations of human fathers. Their failings could serve to highlight the fullness that could be found in God alone. People were meant to be able to have such absolute confidence in their fathers, and only the fall made that not be the case. But in God, hearts wounded by the lack of a perfect earthly father could be healed. They could find in him what even very good earthly fathers could not always provide.
hallowed be thy name
The name of God was, is, and will be holy in itself. But we ask that it be known to be such in the world. Only on the basis of the world's recognition of the holiness of God can the world be ordered to him. And only when it is properly ordered to its cause and destiny can it reach its potential. Only then will people truly flourish. But we especially need the name of God to be hallowed in our hearts and in our lives. Unless this happens our prayers will be deficient. We'll approach him as though we're merely asking for the help of some powerful being within reality, with his own needs and limitations. Instead, we're meant to pray on the basis of his absolute transcendence. It is precisely this that means he is so fully present and able to help us. If we do not recognize God's holiness we'll try to use him for our own ends rather than asking him to use us for his purpose in accordance with his will. We'll necessarily feel limited in what we can ask if we imagine he himself has a limited capacity to respond. We'll only 'bother' him with prayers that seem especially 'important'. Even then our confidence will be lacking that he can balance these out against the needs of so many others.
thy Kingdom come
The Kingdom is present in the Church, the Body of Christ, where the rule of the king holds sway. But it is still imperfectly present. We still often fail to live as the king would have us live. We do not love consistently or well in the way he commanded. So we pray that the Church can fully embody its identity as the place where the king himself reigns. We pray too that she spreads more and more so that all people can be set free from the kingdom of darkness and experience the goodness of the Kingdom of God. But this means that, above all, we need the Kingdom to come more fully within each of us. Only when we as individuals open ourselves to this petition will the Church become what she is truly meant to be. When this does happen the Church will become more attractive to the world and effective in her mission. But it must begin at the level of individual hearts.
thy will be done,
on earth as it is in heaven.
Heaven is so good because in it the will of God is perfectly fulfilled. And this can be so on earth as well, as least to a much greater degree than it is now. But it will only come to pass when we recognize that his will is that of a loving and holy Father. We tend to doubt the goodness of his will and to wonder if he really has our best interests at heart. But we learn the goodness of his will from reflecting on the fact that, in heaven, where it is carried out in fullness, all desires are fulfilled, and heart finds rest.
Give us this day our daily bread;
After asking for a correct heart and mind toward God we finally have a sufficient basis to ask him for our needs, not out of fear our desperation, but rather based on our hope and trust in him. He is the one who knows what we need better than we ourselves know it. We can now ask him for our daily natural and spiritual needs, for help to live free from sin and unforgiveness, protected from temptations to great for us, and live safe from the power of the evil one. We realize how much greater his will is than our own by the way he consistently over-delivers on our requests. Just one example will suffice. We ask for enough bread to eat each day, but he responds by offering us the Body and Blood of his Son to freely receive.
The works of his hands are faithful and just;
sure are all his precepts,
Reliable forever and ever,
wrought in truth and equity.