What does this mean? “This means that I should be certain that these petitions are pleasing to our Father in heaven, and are heard by Him; for He Himself has commanded us to pray in this way and has promised to hear us. Amen, amen means ‘yes, yes, it shall be so'” (SC, The Conclusion).
The beginning and end of something usually look quite similar. When moving into a new home, you have boxes filled with all your belongings, and as you move out your belongings are all back in boxes. At the beginning of a play, the curtain goes up; and at the end, it comes down. At the beginning of college, you tackle the unknown as a neophyte at the academy; and at the end of college, you tackle the unknown as a neophyte in the workforce.
The Lord’s Prayer is like this, too. We begin with “Our Father,” looking heavenward to our Father in heaven. Then we move down to earth as we pray for our bodily and spiritual needs. And now, here at the end, we gaze heavenward again as we acknowledge that the kingdom (and all kingdoms), all power, and all glory belong to Him for all eternity. And so, we end our prayer with, “Amen.” What do we mean when we say “amen”? Luther explains it quite well:
Finally, mark this, that you must always speak the Amen firmly. Never doubt that God in His mercy will surely hear you and say “yes” to your prayers. Never think that you are kneeling or standing alone, rather think that the whole of Christendom, all devout Christians, are standing there beside you and you are standing among them in a common, united petition which God cannot disdain [hence the “our” in “Our Father”]. Do not leave your prayer without having said or thought, “Very well, God has heard my prayer; this I know as a certainty and a truth.” This is what Amen means.
LW 43:198
Therefore, when you say “amen” to this or any other prayer, you are saying, “I know God has heard me, and I know He will give me His ‘yes’ according to His good and gracious will.” Especially when you pray the Lord’s Prayer, He will answer each of this in the affirmative; for these petitions are not merely things we ask for because we need them, chalking it up to God’s heavenly coin flip. Rather, God promises to answer each of these petitions with His divine “yes.” We call it the Lord’s Prayer because “Lord’s” is a possessive noun—this prayer is His. Our gracious Lord would not give us a prayer His Father would not answer. Rest assured, then, that your Father in heaven hears your beloved voice, and He responds, “Yes, my dear son. Yes, my lovely daughter. It shall be so.”
The Lutheran Column 