Ethos is all about judging character. In Aristotle’s Rhetoric, it’s one of the three types of appeals you can make to your audience (along with pathos and logos). Your ethos is your trustworthy factor.
So let’s say you’re giving a speech about the health benefits of dessert. Your audience might be wondering—do you know what you’re talking about? Are you serious? And how do we know you’re not working for the Ice Cream Lobby of America?
To get your audience on board, you might talk about your research on sugar, or about the book you wrote, Ice Cream and the Balanced Diet. (Seriously, can someone write that book?) Or, you can go one step further and appeal to their moral character, which is really what ethos is all about. That's right, just tell them that eating ice cream makes them upstanding citizens. Boom. Argument won.