Why Do People Say “Amen” at the End of a Prayer?

According to Merriam-Webster, the interjection amen is "used to express solemn ratification (as of an expression of faith) or hearty approval (as of an assertion)." It is often interchanged with phrases such as so be it.

The original word in Hebrew bears relation to other words denoting security and steadfastness, but the fact that it was borrowed into other languages as amen (rather than translated into a meaningful phrase) demonstrates that any use of the word in Hebrew beyond solemn ratification had already been lost by the Common Era.