The feedback technique of echoing the speaker's message back to him in your own words is called

Echo effect.

The echo effect is a tool in social interactions that involves restating a speaker's words or message back to him or her. The echo effect is a useful and effective social tool wherein, you can restate a speaker's message to clarify it and demonstrate your understanding of it. Furthermore, people who adopt this technique in social interactions are perceived as more empathetic and caring compared to people who do not use this technique.