What does ''Amen'' mean?

Many of us grew up saying prayers and, in imitation of the adults around us, we learned to end them by saying ''amen.''
Amen is commonly used after a prayer, creed, or other formal statement. It is spoken to express solemn ratification or agreement. It means ''it is so'' or ''so it be,'' ''Verily'' and ''Truly''. It is usually used as an expression which declares a statement as true. Amen is etymologically derived from the Hebrew amen, which means ''certainty,'' ''truth,'' and ''verily'' and is a shared response to liturgical rites and a means of affirming sacred scripture.

Why Do Muslims Say Amen?
It is a known fact (well almost) that this word can be found nowhere in the Quran. Albeit the word 'Amen' (Ameen) is never found in text form in the Quran as a culmination to prayer, there is also no prescription in the Quran that only Quranic words can be recited in prayer. In fact, in formal prayers, many prayers are recited which are not found in the Quran, such as the Tashahhud. Therefore, rather than dismissing the term 'Amen' as non-Quranic, it is far better to understand what it means or implies and to make an 'informed' decision whether to make use of it in one's prayer or not.
Any use of amen in Islamic prayer is considered optional (sunnah), not required (wajib). The practice is based on the example and teachings of the Prophet Muhammad, peace be upon him. He reportedly told his followers to say 'amen' after the imam (prayer leader) finishes reciting the Fatiha saying, 'Ghair-il-Maghdubi 'Alaihim Walad-Dallin \[i.e. not the path of those who earn Your anger, not the path of those who went astray ' (1:7)], because: "If a person's saying 'amen' at that time coincides with the angels saying 'amen', his previous sins will be forgiven."
We note a long tradition with those that align themselves with the faith of Abraham making use of such a term as a culmination to a prayer.
There are no prescriptions or prohibitions as to what should or should not be recited in prayer. Meaningful prayer which draws from Quranic narratives and supplements it with personal prayer does not contravene any verse of the Quran. However, with any recitation, one should always make use of meaningful, goodly words which have purpose and touch the core of one's spiritual faculties.
Recitation should be understood, as utterance without meaning is in breach of the Quran (4:43) and the underlying wisdom not to approach prayer - hatta ta'lamu ma taqulun (until you know what you are saying).
It is far better to understand the words we make use of in our prayer and to make an informed decision as to whether we deem it appropriate to make use of them or not

en.shafaqna.com