Stephen Byerley is either a robot or a very good human. And we can't know which. He's running for mayor of some city. (Even that's not clear. Byerley lives in a place called Evanstron (192), which doesn't exist, but which might be a new city. Or maybe it's a suburb of Chicago or New York. Or even LA, which has always been popular with robots.)
We learn quite a bit about Stephen Byerley, both from what people say and what we see. For instance, Francis Quinn tells us that Byerley is "the most capable and intelligent prosecutor I have ever known" (22). And we see Byerley in action that shows how capable he is; it's just a minor thing, but notice how he knows that Susan Calvin has an apple in her purse (90). Oh, and then there's the whole way he turns Quinn's rumor against him and gets elected mayor (of whatever city).
But we're interested in Byerley not because he's smart but because he might be a robot—because he's so good and moral. This is the point that Calvin makes over and over: the only way to tell a human from a robot is that the human is probably a jerk. (Oh, well, you could take an x-ray photo or dissect the body, but Byerley doesn't let those two possibilities happen.) And Byerley isn't a jerk, not in any way. (And Calvin, Lanning, and Quinn go through a bunch of possibilities of how Byerley might be a jerk or at least jerk-like (133-160).)
What does this robot tell us about robots? Whoa, whoa, whoa, let's not be so quick to judge—we don't even know that he is a robot. But the fact that he might be tells us clearly that robots are kind of like good people.
Also, Stephen Byerley is so good at his job that he works his way up to World Co-Ordinator in the story "The Evitable Conflict."