The Greek word "ethos" refers to a person's defining character. In the context of rhetoric, ethos can be thought of as persuasion through credibility, as Andrew Dlugan explains in his "Six Minutes" article. Using ethos in persuasion means to qualify a statement with credentials. An argument might be prefaced by an author's degrees and achievements. Ethos can also be used in the way in which an author communicates. If her voice is authoritative --- if she sounds like an expert --- the audience is more apt to give her the credence of an expert.
Pathos is the use of emotion in persuasion. Authors often use anecdotes trying to get an audience to empathize with their position. In a sense, much of literature is an essay that uses pathos to make an argument. We empathize with notable characters, so we see things from their point of view. Similarly, in essays that use pathos, we're compelled to "put ourselves in someone else's shoes."
"Logos" is an Ancient Greek term meaning "word" or "logic." This is the most fundamental tool in essay writing: Make a statement, then support it with evidence. The supporting argument is the "logos." The author walks the audience through the logic of her assertion. If the logic cannot be criticized or is not in error, the conclusion is generally accepted.
Statistics are closely related to logos. Statistics by themselves, aren't necessarily used to support a claim. Without the context of a logical argument, they may be little more than organized data. Within the context of an argument, statistics can provide the logos of an essay; they can solidify an argument. The source of the statistics employs ethos. The narrative invokes pathos. At their heart, though, they appeal to our logic.