When someone's angry at you and you want them to stop being angry, you can use the word "Listen" to introduce your sentence. For example:
Listen, I don't want to fight about this.
Listen, I'm sorry, OK?
Listen, I'm willing to let this go if you are.
"Listen" at the beginning of a sentence can have other functions, too. It can introduce an uncomfortable topic like this:
Listen, do you mind if I crash on your couch for a night or two?
In general, "Listen" signals that you're expressing your real emotions about something.