Logos means word, speech or reason. It is the use of reason and reasoning, whether inductive or deductive, to construct an argument. In persuasion, logos is the logical reasoning behind the speaker's statements. Logos refers to any attempt to appeal to the intellect, to logical arguments.
We can recognize the logos feature in Brutus's speech, shown in the question above, since Brutus calls for logical reasoning to justify his betrayal of Caesar.