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 you want to learn more, book below: