Plain terms: It means they feel unheard. And hurt. They want you to understand their side, and to prove that you understand their side by changing your behavior.
First step in your response: Breath out. The out breath is more likely to deescalate you. An in breath will give your body resources to argue back.
Second step: Ask what do they need from you.
Third step: Take a 15 minute break from the conversation to take a break and consider what they asked.
Not knowing the ins and outs of your relationship, I can't advise that you automatically shift and do what they ask. Chances are you also need their behavior to change. If the above steps doesn't make enough positive difference in your life after a few weeks, get me on a call and we will see what else needs to happen.