The word amen means so let it be or it is true. In the Old Testament when the people responded by saying amen they attested to the sentences which they heard were true, just, and certain.
Saying amen is a way to finish our prayers. When Christians say amen at the end of our prayers, they are following the model of the apostles. They are asking God to let it be as they had prayed.
John 14:12-14 NKJV
“Most assuredly, I say to you, he who believes in Me, the works that I do he will do also; and greater works than these he will do, because I go to My Father. And whatever you ask in My name, that I will do, that the Father may be glorified in the Son. If you ask anything in My name, I will do it.”
1 John 5:14-15 NKJV
“Now this is the confidence that we have in Him, that if we ask anything according to His will, He hears us. And if we know that He hears us, whatever we ask, we know that we have the petitions that we have asked of Him.”