Matt is presumably the ex-boyfriend of Ann Marie, who is a waitress at the Black Spur, a place which he goes to in order to confront her.
After Ann Marie has a one-night stand with Dean Winchester, Matt arrives at the bar they are both at and drags her outside. He starts complaining and asking her where she had been. This draws the attention of Dean who follows them outside.
Dean asks if this is Matt and when it is confirmed, Dean begins beating Matt on the hood of a car. Dean then warns him never to come near nor contact Ann Marie again.
Ann Marie later confesses that she was touched by Dean's actions, since no one ever did something like this for her, but she is aware that Dean just beats people up all the time, and it has nothing to do with honor.