A more elaborate explanation as to why it is a perfect prayer can be found in The Perfect Prayer
by Fr. John A. Hardon, S.J.
Additionally, in http://www.how-to-pray-the-rosary-everyday.com/our-father-prayer.html
we have this:
You offer yourself to God and ask Him for the best things for yourself and your family and friends.
Let's look closer at each of the phrases of the Lords Prayer.
It is led by a greeting "Our Father..." then followed by seven requests:
"Our Father who art in heaven" You belong to God. He created you and watches over you. He wants you to live with Him in heaven forever.
"hallowed be Thy name," You pray that God will be respected by all
"Thy kingdom come," You pray that God will be loved and worshiped throughout the world
"Thy will be done on earth as it is in heaven," You pray that God's laws will be followed on earth as willingly as they are followed in heaven
"Give us this day our daily bread," You ask for your spiritual and physical needs
"and forgive us our trespasses as we forgive those who trespass against us," You ask God forgive your sins you have committed against His laws and promise Him that you will forgive people who cause you harm
"and lead us not into temptation," You ask God to keep you safe from all people and places that may lead you to sin
"but deliver us from evil," You ask God to protect you from both physical and spiritual harm The Lords prayer asks God to grant you peace and when praying the Lords Prayer, you ask for all your spiritual and physical needs.
It truly is the perfect prayer.
Over time I have contemplated on this prayer and I have come to see that there are other reasons why it can be considered a perfect prayer. I see in this prayer acknowledgement of the Father, Son and the Holy Spirit.
The first verses acknowledge the Father. "Our Father who art in heaven, hallowed be Thy name,"
The next two verses acknowledge the incarnate Son who revealed to all God's kingdom, and who perfectly showed us how God wants us to live -- in total obedience to His will. Thus in this Son, God's kingdom had come and the Son did his Father's will on earth as it is being done in heaven,
"Thy kingdom come, Thy will be done on earth as it is in heaven,"
God in the Person of the Son then instituted the Eucharist and the practice is carried on to the present and so we have this request being fulfilled: "Give us this day our daily bread". The Son also forgave sin and urged us to forgive those who offend us, "Forgive us our trespasses as we forgive those who trespass against us". In the Church we treasure not only the Eucharist but also the sacrament of Reconciliation which the Son instituted.
Then there is acknowledgement of the Holy Spirit who we pray to for guidance and spiritual strength, "And lead us not into temptation, but deliver us from evil." We ask not be tested and if we fall, as we are most likely to, we ask for His grace to seek deliverance.
So while addressed to the Father, this prayer allows us to contemplate the the Holy Trinity -- the unity of Father, Son and Holy Spirit.
This is, indeed, the perfect prayer.