(in order of appearance)
There is also an unnamed interlocutor. The one fact we learn about the interlocutor is that both he and Socrates have spent time with Lysimachus (the son of the statesman Aristides). In Meno, Socrates notes that Meno has spent time with Lysimachus; so the author here seems to be taking account of the fact that Lysimachus is also a character in Laches, so Socrates knows him, too.
The Plot and The Thought
Socrates opens the dialogue by asking his interlocutor whether virtue can be taught, and if not, whether people are virtuous by nature. His interlocutor says he doesn't know, so Socrates leads him to the consideration that if virtue can be learned it would have to be from good men, and he asks who the good men of the city are. The interlocutor names Thucydides (the opponent of Pericles, not the historian), Themistocles, Aristides, and Pericles. But for none of these can we name a definite teacher of virtue, so we have to consider their students. But there don't seem to be any of those, either.
Further, if good men are just, it seems they would want to help rather than harm, and would be happy to communicate their goodness. But if we look at Cleophantus, the son of Themistocles, or Lysimachus, the son of Aristides, or Paralus and Xanthippus, the sons of Pericles, or Melesias and Stephanus, the sons of Thucydides, they don't seem any more virtuous than anyone else. So it looks like virtue can't be taught.
This raises the opposing question: is virtue something had by nature. Socrates notes that there is a skill by which one knows the nature of good horses (horsemanship) and a skill by which one knows the nature of good hounds (huntsmanship) and a skill by which one knows good money from counterfeit (money-changing), and a skill by which one knows good traits of the human body (athletics), so if virtue were a matter of nature, one would think that there would be a corresponding skill for knowing good men. The interlocutor doesn't know what it could be, and Socrates remarks (as in Meno) that if we had it, you'd think that the city would find the boys with good natures and take special efforts to protect them. So that's a sign that virtue is not had by nature, either.
The interlocutor asks how men come to be virtuous, then, and Socrates responds that it is by divine allotment:
I don't think it's very easy to explain this. my guess, however, is that the possession of virtue is very much a divine gift and that men become good just as the divine prophets and oracle-mongers do. For they become what they are neither by nature no skill: it's through the inspiration of the gods that they become what they are. Likewise, good men announce to their cities the likely outcome of events and what is going to happen, by the inspiration of god, much better and much more clearly than the fortune-tellers. Even the women, I think, say that his sort of man is divine, and the Spartans, whenever they applaud someone in high style, say that he is divine. And often Homer uses this same compliment, as do other poets. Indeed, whenever a god wishes a city to become successful, he places good men in it, and whenever a city is slated to fail, the god takes the good men away from that city. So it seems that virtue is neither teachable nor natural, but comes by divine allotment to those who possess it. (379c-d)
This is mostly a summary of the end of Meno, but there are two ideas that go beyond that dialogue: that "good men announce to their cities...what is going to happen...much more clearly than the fortune-tellers" and that the rising and falling of cities is connected with the allotment of virtue.
Quotations are from Mark Reuter's translation in Plato, Complete Works, Cooper and Hutchinson, eds., pp. 1694-1698.