Baruch Adonai L'Olam is a paragraph recited during Shacharit in Pesukei Dezimra following Hallel. The paragraph consists verses beginning with the word Baruch (ברוך), Hebrew for Blessed, which states that God is a source of blessing. It is recited following Hallel as a way to relate Hallel to blessing.
The word Amen is recited twice in the first verse as an emphasis on this word. The word Amen can have three meanings: to accept a vow upon oneself, to acknowledge the truth of a statement, and the expression of hope that a prayer will come true.