How do these words land on you: “I hear you”, “I understand you”? To some people, they mean the same thing.
“I hear you”: Some people take that as the one saying those words is impatient or that they are not really trying to get your point and they want to jump in with their point of view. It often connotes an unspoken, “but I sure don’t agree with you!”
Many people feel the words “I understand you” are more empathetic. This is saying that “I’ve paid enough attention to understand what you’re saying.”
Of course, the context and the nonverbals (such as the tone and body language) are very important.
Ideally, you’d show that you really ‘get’ what they are expressing by paraphrasing “So what I understand is that …. Is that it?” “I wonder if what you are saying is ….”