"Father, where did the prayer after the Lord's Prayer during Mass come from? I don't ever remember it from before."
This questioner is obviously asking about the Libera Nos, the embolism (insertion) which in the New Order of Mass (1970) is said aloud by the priest. In the Traditional form of Mass, the Libera Nos was said quietly by the priest as he prepared for the fraction of the Sacred Species (except at the Mass of the Presanctified on Good Friday, when it was said aloud). To begin with, let's look at the text itself:
"Deliver us, Lord, we pray, from every evil, graciously grant peace in our days, that, by the help of your mercy, we may be always free from sin and safe from all distress, as we await the blessed hope and the coming of our Saviour, Jesus Christ." (trans., ICEL 2010)
The more traditional form, which was said up until the Missal of Paul VI said:
Deliver us, O Lord, we beseech Thee, from all evils, past, present, and to come; and through the intercession of the glorious and blessed Mary, ever Virgin, Mother of God, together with They blessed Apostles Peter and Paul, and Andrew, and all the Saints, grant of Thy goodness peace in our days, that aided by the riches of Thy mercy, we may be always free from sin, and safe from all disquiet. Through the same Jesus Christ, Thy Son, our Lord, who liveth and reigneth with Thee in the union of the Holy Ghost, God. World without end. Amen. (trans. by Rev. J. Rea, 1961)
[Those who know me can probably tell just from this which prayer I would prefer to say, but I digress.]
Not having a wide range of liturgical reference books at my disposal, I am limited in the explanation that I can give. No doubt some of my liturgically-inclined friends might be able to shed more light on the origin and development of this prayer. Both Jungmann and Fortescue make reference to this embolism as being extremely ancient. There is probably enough evidence to support an assertion that this prayer was in existence by the time of, if not before, Pope St. Gregory the Great (+604). Little is said of its purpose or of its particular origin. However, it seems to be a very logical prayer following the last words of the Lord's Prayer, "But deliver us from evil." In all the Eastern rites, and in the rites at Paris (prior to the 20th century reform), the Lord's Prayer was said by the whole congregation, as it is today in the modern Roman Rite. In the ancient Roman Rite, however, only that final phrase, "But deliver us from evil," was said by the people. The rest of the prayer was said alone by the priest.
As I said, it seems a logical following that the prayer immediately after "But deliver us from evil" should carry on that petition of deliverance from evil and expand it to invoking the intercession of Mary and the Saints. The saints mentioned naturally varied from place to place. It seems logical that the Mass at Rome would invoke Peter, Paul, and Andrew. In Milan, Ambrose is added. Fortescue mentions that "in the middle ages, the celebrant was expressly allowed to add any Saints he liked..." (The Mass, 364).
In our modern rites, this prayer is far more pronounced, namely because it is said aloud by the priest. Although, most scholars would lament the shortened form, it still carries with it that continuation of a plea for deliverance from the trials and tribulations of this life. What makes it a bit bizarre in the modern context, however, is the addition of the traditionally Protestant appendage to the Lord's Prayer, "For the kingdom, the power, and the glory are yours, now and forever." Both its placement and its very insertion into the Roman Rite is rather jarring, and it seems to take a great deal away from the significance of the Libera Nos.
I'm sure this doesn't come close to answering the question that was posed. But, as I said, the liturgical resources at my disposal are rather meager at the moment, so I'm making due with what I've got! In any event, the Libera Nos (even in its present, shortened form) is indeed ancient, and it remains a part of Catholic patrimony that has (more or less) stood the test of time.