Converse has two different meanings:

1. To have a conversation with someone. When two people converse, they talk back and forth, sharing ideas and listening to each other. You might converse with your grandmother about her childhood, or converse with a friend about your favorite books. The word suggests thoughtful exchange: when people converse, they're genuinely discussing ideas and paying attention to what each person says. Teachers might ask students to converse about a story they've read, meaning they should discuss it seriously and listen to different viewpoints.
2. In mathematics and logic, the converse of a statement reverses its parts. If your original statement is “If it's raining, then the ground is wet,” the converse would be “If the ground is wet, then it's raining.” Notice how the converse isn't always true: the ground could be wet because someone turned on a sprinkler. Understanding converses helps you think more clearly about cause and effect. Scientists and mathematicians pay close attention to converses because reversing a true statement doesn't automatically make the converse true.