The dialogue, one grouped around the trial of Socrates, starts with Meno asking Socrates, rather abruptly, "whether virtue is acquired by teaching or by practice".
Socrates replies that he doesn't know what virtue is; in fact, he's never known anyone who did know. Meno explains that there is the virtue of the mother, and the virtue of a man, and the virtue of a child, et cetera. But, Socrates notes that this list of all the virtues doesn't explain what's common between them. After quite a bit of light joking about how to define things, Meno comes up with the following: "virtue is to delight in things honorable and have the ability to get them."
This is better; but, if honorable things are the same as good things, then everyone wants what is good. The key must be in the power to get them. Yet, he must get them justly. So, now we're back to enumerating the parts of virtue!
Now, they're more confused than ever. In a famous section of the dialogue, Socrates explains that this is a part of knowledge. He has heard that we have immortal souls that pass through successive periods of existence, perpetually remembering and forgetting. All of nature is kindred and each has the seed of all knowledge within them. Learning, then, is a process of remembering. In a famous section, Socrates demonstrates this by eliciting certain geometrical relations- specifically, that the square of the diagonal is double the square of the side- from a totally uneducated slave.
Socrates knows that virtue is a good; but he does not think it is a sort of knowledge because he has never known any teachers of virtue. Therefore, virtue must not be teachable.
In a section that amounts to foreshadowing, they ask the well-to-do Athenian gentleman Anytus who to go to in order to be taught virtue. Socrates suggests the sophists, which angers the man. He then recalls several honorable men of old: Themistocles, Pericles, and so on; and points out that none of them had honorable sons, so they must not have taught virtue. Anytus is outraged to hear the old Athenian heroes slandered and leaves, warning Socrates to watch his tongue. He will participate in the trial of Socrates and there's an interesting critique implied about the sort of person who believes that virtue adheres unquestioningly to certain groups, so referring to "Athenian gentlemen", for example, settles the question.
If virtue is not a sort of knowledge that can be taught, and it's not innate- since we don't generally recognize it in children- couldn't it come to us some other way. Socrates suggests that virtue might really be "right opinion", which really cannot be taught, as it's more instinctual; but which is as good as knowledge for all practical purposes? Socrates proposes that great statesmen have a sort of instinct for right behavior that is divinely given- a sort of revealed instinct. Like prophets, they are divine and possessed by God.
Notes: I like the idea of virtue as "right opinion" because it gets at the fact that virtue isn't easily pinned down or transmitted. A virtuous person today can become unvirtuous tomorrow. I understand this as more akin to a state of mind or a disposition. Aristotle would similarly define virtues as states of being between two extremes- courage is the state between cowardice and foolhardiness, for instance.
It also gets at the fact that we often act virtuously without really knowing why, and then later try to explain it through ethics. There's something... pre-rational about ethical behavior that is akin to how we respond to art- usually there's a nonverbal emotive response which we later try to verbalize. Hemingway said that "evil" is what we feel bad about afterwards and I think there's something to that.
I like this answer, but it's lousy for Meno, who is basically a sophist. He wants an answer that can be easily pinned down and doesn't get it. Socrates is making fun of him throughout the dialogue, whether he realizes it or not. What he's trying to do, and he says as much, is put Meno in a state of aporia- puzzlement, which is intended to be salutary. As Socrates puts it, aporia shows the person that what he thought he knew, he doesn't really know; this makes him want to search for the answer. It is destabilizing. However, for a lousy student like Meno- who just wants to be fed the answers- it is frustrating to be "torpedoed" out of any certainly. Unfortunately for him, aporia is central to Socrates' style.
They don't exactly end in a state of aporia, but their definition is marked by this vagueness. Saying that virtue is divinely inspired right opinion serves mostly to disprove Meno's two options: virtue as innate and virtue as taught; it's neither, but it doesn't exactly clear things up for us. However, it does open the way for a link between the nonverbal "irrational" or subconscious and divine revelation. Freud, of all people, almost made way for this connection- a sub-subconscious, so to speak, that would correspond to divine revelation. But, as an atheist, he backed off. Socrates does not.