From aman (H539, to trust/be firm), amen is a declaration of absolute agreement and trustworthiness. It means 'Let it be so — I stake myself on this truth.' Used to confirm a word just spoken, ratify a covenant, or affirm a blessing/curse.
Amen is borrowed directly into Greek and then every language of Christianity. In the Psalms it closes doxologies (Pss 41, 72, 89, 106), affirming that what was just declared about God is absolutely true. Jesus famously inverted the usage — 'Amen, I say to you' — placing it at the beginning to mark his own words as divine authority.