Logos (Greek for "word") refers to the internal consistency of the message--the clarity of the claim, the logic of its reasons, and the effectiveness of its supporting evidence. The impact of logos on an audience is sometimes called the argument's "logical appeal."
Ramage and Bean, Writing Arguments, 4th Edition. Allyn & Bacon, 1998, 81-82
Following one of the other meanings of the word, Aristotle, in the Ars Rhetorica, gave logos a different technical definition as argument from reason, one of the three modes of persuasion (the other two modes are pathos (Greek: πάθος), persuasion by means of emotional appeal: "putting the hearer into a certain frame of mind," and ethos (ἦθος), persuasion through convincing listeners of one's "moral character." According to Aristotle, logos relates to "the speech itself, in so far as it proves or seems to prove."In the words of Paul Rahe:For Aristotle, logos is something more refined than the capacity to make private feelings public: it enables the human being to perform as no other animal can; it makes it possible for him to perceive and make clear to others through reasoned discourse the difference between what is advantageous and what is harmful, between what is just and what is unjust, and between what is good and what is evil.
Logos, pathos, and ethos can all be appropriate at different times. Arguments from reason (logical arguments) have some advantages, namely that data are (ostensibly) difficult to manipulate, so it is harder to argue against such an argument; and such arguments make the speaker look prepared and knowledgeable to the audience, enhancing ethos. On the other hand, trust in the speaker, built through ethos, enhances the appeal of arguments from reason.
For someone wanting to learn how to be persuasive, how to direct others to action by words alone, which is preeminently the assigned task for all of those who aspire to political leadership, it would be hard to find a better example of effective rhetoric than Clinton's speech.
Logos, of course, like Ethos, has a different meaning, too, a meaning outside the context of rhetorical technique. "Logos" means "word." It is from words, or as we often say, "mere words," that we construct the world we most immediately inhabit.
Perhaps as an analogy to the human experience, from which we learn the generative power of words, the Gospel of John makes an even greater claim:
In the beginning was the Word, and the Word was with God, and the Word was God. (John 1:1)