From the Greek, "logos" originally meant "word," "speech," "account," or "reason," but over time has taken on a new meaning. Related to philosophy, psychology, etc., it can refer to a plan or an account. The dictionary definition is "the rational principle that governs and develops the universe." (Logo- comes from the Greek, meaning "reason.")
Pathos deals with the expression of the emotional. (In Greek páthos means "to suffer.") It appeals to the emotions of a group when included in a play, for instance.
Ethos deals more with society: the beliefs or customs of a culture. (From the Greek, it means "custom, habit, character"). It deals with one's "guiding beliefs."
So Logos deals with reasoning; pathos deals with emotions; and, ethos deals with the common practices of culture or a group.