There are many ways to appeal to an audience when giving an argument or a persuasive speech. Aristotle outlined three of these appeals, which he called logos, ethos, and pathos. The best arguments combine elements of all three, but many strongly hew to one in particular.
1) Logos: Logos comes from the Greek for "knowledge." The logos appeal refers to the argument itself: the facts, the logic, the reasoning. Giving an argument based in logos may include a lot of hard data and scientific evidence. It may also include empirical evidence and real-life examples—provided they're based more in fact than emotion. A written argument may include many citations. In theory, a well-written argument with a logos appeal will make the audience come away thinking, "that person really knows his/ her stuff."
2) Ethos: Ethos comes from the root that gives us "ethics." The ethos appeal refers to an appeal using one's own character or ethics to convince the audience; in other words, how they build credibility and trustworthiness on a personal basis. An argument with an appeal to ethos may include a lot of information about the writer/ speaker's credentials and background, or it may include specific personal examples where the author/ speaker demonstrated strong morals. A well-done appeal to ethos will make people think, "That person is someone I believe in."
3) Pathos: Pathos refers to emotion. An argument based in pathos is considered the weakest type of argument from a rational standpoint, but often has a strong impact on its listeners. There have been many appeals to emotion in recent political speeches. An argument based in pathos focuses primarily on tone and language and includes many examples that evoke strong feelings (anger, joy, triumph, grief, etc.). Figurative language and vivid descriptions are common. A well-done appeal to pathos will make people walk away thinking, "I feel [emotion] about [issue]."