Euthyphro
Question here is "What is piety?" (my translator Fowler tending to use "piety" or "holiness" interchangeably, whereas the translator used in class tends to stick with "piety"); the dialogue ends inconclusively, the point being that you shouldn't smugly think you know what something such as piety is unless you've given it a lot of thought, and the dialogue is an example of how to go about thinking.
The question is of interest to Socrates not just for its own sake but because he's about to go on trial for his life, one of the accusations being impiety, so it would help to have an idea of what piety is when he faces his accusers. Euthyphro, though certain that he already knows, turns out to be of no help in the matter and ultimately begs out of the conversation.
A basic question that Socrates asks but I think ends up sidestepping: Is something (some behavior) holy because the gods love it, or do they love it because it's holy?
I see this as a question about authority. Is something holy on authority of the gods, or is holiness holy on its own authority? And on what authority or whose authority can we say what holiness is? 2,400 years later, such questions still seem like good ones;* that is, not easy to answer, though looking back 2,400 years (how time flies when you're doing philosophy!), I think Plato is asking them wrong, or is asking the wrong questions. He's far too either/or in the choices he give us and is wrong to think that the question of authority needs or can get a general, universal answer.
Socrates: We speak of being carried and of carrying, of being led and of leading, of being seen and of seeing; and you understand - do you not? - that in all such expressions the two parts differ one from the other in meaning and how they differ.
Euthyphro: I think I understand.
Socrates: Then, too, we conceive of a thing being loved and of a thing loving, that the two are different?
This actually sets the conversation going in a poor way, from which it never recovers, the difficulty being that it leaves out a third possibility, that something is visible yet unseen owing to no one having yet looked. And furthermore, the question as to whether a loved thing deserves to be loved doesn't really get posed in this framework, even though that's a question that Socrates seems to be raising in regard to piety.
Here's Socrates' argument at length
Socrates: We speak of being carried and of carrying, of being led and of leading, of being seen and of seeing; and you understand - do you not? - that in all such expressions the two parts differ one from the other in meaning and how they differ.
Euthyphro: I think I understand.
Socrates: Then, too, we conceive of a thing being loved and of a thing loving, that the two are different?
Euthyphro: Of course.
Socrates: Now tell me, is a thing which is being carried a carried thing because one carries it, or for some other reason?
Euthyphro: No, for that reason.
Socrates: And a thing which is being led is led because one leads it, and a thing which is seen is so because one sees it?
Euthyphro: Certainly.
Socrates: Then one does not see it because it is a seen thing, but, on the contrary, it is a seen thing because one sees it; and one does not lead it because it is a led thing, but it is a led thing because one leads it; and does not carry it because it is a carried thing but because one carries it. Is it clear Euthyphro, what I am trying to say? I am trying to say this, that if anything becomes or undergoes, it does not become because it is in a state of becoming, but it is in a state of becoming because it becomes, and it does not undergo because it is a thing which undergoes, but because it undergoes it is a thing which undergoes; or do you not agree to this?
Euthyphro: I agree.
Socrates: Is not that which is beloved a thing which is either becoming or undergoing something?
Euthyphro: Certainly.
Socrates: And is this case like the former ones; those who love it do not love it because it is a beloved thing, but it is a beloved thing because they love it?
Euthyphro: Obviously.
Socrates: Now what do you say about that which is holy, Euthyphro? It is loved by all the gods, is it not, according to what you said?
Euthyphro: Yes.
Socrates: For this reason, because it is holy, or for some other reason?
Euthyphro: No, for this reason.
Socrates: Is it loved because it is holy, not holy because it is loved?
Euthyphro: I think so.
Socrates: But that which is dear to the gods is dear to them and beloved by them because they love it.
Euthyphro: Of course.
Socrates: Then that which is dear to the gods and that which is holy are not identical, but differ one from the other.
Euthyphro: How so, Socrates?
Socrates: Because we are agreed that the holy is loved because it is holy and that it is not holy because it is loved; are we not?
Euthyphro: Yes.
Socrates: But we are agreed that what is dear to the gods is dear to them because they love it, that is, by reason of this love, not that they love it because it is dear.
Euthyphro: Very true.
Socrates: But if that which is dear to the gods and that which is holy were identical, my dear Euthyphro, then if the holy were loved because it is holy, that which is dear to the gods would be loved because it is dear, and if that which is dear to the gods is dear because it is loved, then that which is holy would be holy because it is loved; but now you see the opposite is the case, showing that the two are entirely different from each other. For the one becomes lovable from the fact that it is loved, whereas the other is loved because it is itself lovable. And, Euthyphro, it seems that when you were asked what holiness is you were unwilling to make plain its essence, but you mentioned something that has happened to this holiness, namely that it is loved by the gods. But you did not tell as yet what it really is.
*Except we're likely to ask the question in regard to "value" rather than "piety": is something valuable because we value it or do we value it because it's valuable?