Here "A certain woman" introduces a new person in the story. Alternate translation: "There was a woman named Lydia" (See: [[rc://en/ta/man/jit/writing-participants]])
For the Lord to cause someone to pay attention and believe a message is spoken of as if he were opening a person's heart. Alternate translation: "The Lord caused her to listen well and to believe" (See: [[rc://en/ta/man/jit/figs-metaphor]])
Here "heart" stands for a person's mind. Also, the author speaks about the "heart" or "mind" as if it were a box that a person could open so it is ready for someone to fill it. (See: [[rc://en/ta/man/jit/figs-metonymy]] and [[rc://en/ta/man/jit/figs-metaphor]])