Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Saying ‘Ameen’ is in reality a supplication, because the meaning of Ameen is “O Allah do that or respond to this call”.
Therefore, if someone listens to a supplication directly from a person or from a tape and says ‘Ameen’, it is as if he made the supplication to Allah to accept and respond to that call which is mentioned, and a Mu’min is making the Du’a in reality, and if it is confirmed that saying ‘Ameen’ is a Du’a, therefore raising the hands when a supplication is made is an etiquette of Du’a.
In principle it is a Sunnah to raise one’s hands when a Du’a is made, except in case when there is an evidence, that forbids raising hands in Du’a like when the Imam raises his hands during Jumu’a Khutba.
In a Hadith: “Allah is generous and shy, and is shy (not to reward a person who raises his hands) to turn back the hands raised for His Bounty without something (reward)”. [Reported by Ahmad]
Allah knows best.