Probably over half of the communications problems I've seen at work are because people don't follow this basic practice. They respond based on what they understood, not based on what the speaker was saying.
As one book I read put it: You should be able to reflect their world view back to them as if you yourself are advocating for it (even if you completely disagree). When you do this, they'll believe you understand them. For many people, only then will they listen to your critiques.