Ethos is like the appeal to ethics, which means to convince an audience of the author's credibility or character (This can also be applied outside of literature texts as well)
Ex: Say if you went to the doctor and she gives you a prescription for a pill to make you feel better. And she says "As a doctor, I am qualified to tell you that this treatment will likely generate the best results." More or less likely you (or the person being treated) would then take the prescription since the doctor has persuaded you to trust his/her advice.