What is the purpose of using pathos in an argument?

Manipulation. For instance if you are crying because your parents won't allow you to do something then most likely they'll let you do it (eventually).

Ethos is an appeal to ethics, and it is a means of convincing someone of the character or credibility of the persuader. Pathos is an appeal to emotion, and is a way of convincing an audience of an argument by creating an emotional response. Logos is an appeal to logic, and is a way of persuading an audience by reason.