This is a doxology, a prayer of praise, often threefold, to God or the Trinity such as the "Glory be" we commonly pray. Doxologies are used frequently in our prayer.
The doxology at the end of the Lord's Prayer appears in some early biblical manuscripts. Some have "For thine is the kingdom and the power and the glory forever. Amen." Some omit only the Amen; others have the Amen but omit either "kingdom" or "power." In some texts, it was in the margin or in the appendix. Of course, some don't have it at all.
Why this difference? Simply because early manuscripts were hand-copied. These human copiers made some mistakes, often because the text from which they were copying wasn't clearly visible. Also, the earliest texts were not neatly divided into words, sentences, verses and chapters as ours are today.
So, especially in languages that use characters rather than letters, it could be difficult to tell where one word ended and another began. In addition, the texts from which they copied varied according to the area in which they originated, somewhat as our different translations do today.
It seems the doxology was used in the early liturgy of the Church by some Eastern Roman Empire Christians. There is some evidence of its use in the Didache (The Doctrine or Teaching of the Twelve Apostles). This was a first century (about 65-80) document which formulated rules of Christian conduct and of the ministry of the sacraments of Baptism and Eucharist. It was highly regarded by the early Church Fathers (usually Bishops who were great thinkers and writers).
There is a connection with Henry VIII for, in 1541, he decreed it should be used. My sources indicate that this was while he was still in good standing with Rome; remember he had been given the title "Defender of the Faith" by the pope. Later, it was removed from Catholic use and retained by Protestants.
Since the revision of the Mass, this doxology has been added to the Lord's Prayer. However, before the doxology, the Lord's Prayer, which is prayed by all, is followed by a prayer by the priest alone: "Deliver us O Lord, from every evil and grant us peace in our day. In your mercy, keep us free from sin and protect us from all anxiety as we wait in joyful hope for the coming of our Saviour, Jesus Christ."
The whole congregation then prays: "The kingdom, the power and glory are yours now and forever." Some would consider this as not truly being part of the Lord's Prayer since it is separated from it by the aforementioned prayer.
Could be automatic
If the priest omits this prayer, which is placed in between the Lord's Prayer and the doxology, he must be doing it inadvertently. I imagine that it may be quite easy to do that as, in certain circumstances, we may get accustomed to hearing this ending and so automatically add it to the prayer.
This doxology, when added to the Lord's Prayer, whether it be in the form we use at Mass or in recitation of the prayer alone, is a cry of praise and adoration. It fits well with the sentiments expressed in the Lord's Prayer itself: "Hallowed be your name; your kingdom come; your will be done on earth as it is in heaven."
So, at Mass, do not be afraid to proclaim loudly and with hearts full of joy: "The kingdom, the power and the glory are yours, now and forever!"