Plato routinely gives a dramatic rationale for the occasion of his dialogues. Since there are no stage directions or program notes, this kind of thing has to go into the discussion itself, and is indicated by carefully contrived dialogue.

The “Porch of the King” is the situation of the court in which people are tried. The whole adumbrates the coming piece in the Platonic corpus, the Apology of Socrates.

Dramatically, the parallelism is evocative. It is not entirely clear why Socrates or Euthyphro really need to visit the court prior to their own appearances there: but it does create useful symmetries that echo throughout the dialogue and help put the Apology in context.

While Meletus is the chief prosecutor who will eventually bring Socrates down, it is worth noting that here Socrates is not praising Meletus for who he is or how he acts, but commending the premise on which he claims to be acting — a concern for the youth. In the Apology, Socrates takes him to task for not actually being concerned for these things he claims to have made his care.

One slight grammatical challenge needs to be offered to the West translation here: in 2d2, ὅπως ἔσονται ὅτι ἄριστοι, which West translates as “so that they will be the best” is not strictly a purpose or result clause, but a substantive clause: the sense is more “how they will be best”, hence akin more to an indirect question than a declaration of purpose.

Implicitly, an attack on one’s own father would be considered impiety ipso facto. It is worth noting that in this society, while slaves were widely considered property, they still retained certain practical rights, and hence Euthyphro’s belief that his father acted impiously is not unfounded, but certainly it is in conflict with familial obligations.

A refutation in this context is generally known (in Greek) as elenchus. (Aristotle wrote a treatise that goes by the Latin title De Sophisticis Elenchis.—  in other words, On Sophistical Refutations.)

Euthyphro’s usage here is a curious mix of first and third person, and probably cannot be explained by anything you will find in the translation itself — certainly not West’s. When Euthyphro says “nor would Euthyphro be any different from the many human beings, if I didn't know all such things precisely” (οὐδέ τῳ ἂν διαφέροι Εὐθύφρων τῶν πολλῶν ἀνθρώπων, εἰ μὴ τὰ τοιαῦτα πάντα ἀκριβῶς εἰδείην), this can probably be best understood as a pun on his own name, which means “straight-thinking” or “clear-headed”: i.e., “I (being clear-headed) wouldn't be any different from the normal run of people if I didn’t know all this.”

Socrates suggests that if he is following Euthyphro’s advice, then Euthyphro should be prosecuted by Meletus (and the rest) rather than Socrates himself. This has a certain symmetry with the attempt to hold Socrates responsible for the misbehavior or bad attitudes of those he is credited with influencing. Socrates here is fairly obviously pandering to Euthyphro's vanity.

In a dramatic sense, Euthyphro steps in it here by assuring Socrates that he's just the fellow to address the point. One could well analyze this in terms of the dynamics of some (though far from all) Greek tragedy, in which the protagonist engages in an act of hubris (outrage), thus setting himself up for a downfall. Obviously this does not lead to Euthyphro’s death or destruction, but it nonetheless leads to his humiliation and confusion. (Despite modern usage, the term hubris in Greek does not actually refer to pride, and so one must approach this cautiously.)

Most of Plato’s early dialogues are cast in the form of a discussion about the definition of a term: What is x?. Almost invariably these dialogues fail to produce a stable definition, but wind up in a state called aporia: having the same root as our word “pore”, but prefixed with the negation-marker a, this has to do with finding no way through a problem. Other such dialogues include the Laches, on courage, Theaetetus, on knowledge, Hipparchus, on the love of gain (greed), Charmides, on self-control, and Lysis, on friendship. One of the longest and mosts important of Plato’s dialogues, the Republic, is a similar investigation of the question, “What is justice?” but it soon outgrows its initial specifications and takes in a number of different topics.

Ultimately Plato’s student Aristotle came to a more systematic pattern for the formation of definitions. In order to define any subject x, one needs to provide only two things: its genus (what kind of thing it is) and its specific difference (what distinguishes it from other things of the same genus. There are a number of subtle metaphysical implications buried in this method, but it has remained remarkably robust for centuries. Plato’s approach is somewhat different, though he seems to be striving for the same general effect: he asks what idea or ideal (eidos) it can be referred to (or, in Plato’s terms, that it participates in).

For Socrates (and hence Plato), the defining feature of anything — that which entitles any subject to take the predicate x, is its eidos — its idea (pattern, rationale — the word is rich and complex, and is central to Platonic metaphysics. Aristotle treated the problem in terms of genus (type, kind) and specific difference (what sets this particular thing apart from other species of its kind).

The West translation uses the phrase “the eidos itself by which all the pious things are pious”; the dative Greek relative pronoun ᾧ is used for means, but also relation: it might equally well be rendered as “with respect to which”.

This may well seem somewhat comical as an interlude, but in fact it is connected with at least one of the matters that causes Socrates to be condemned at his trial. One of the charges is that he makes the better argument appear the worse.

Socrates gets at an important set of logical structures here, adumbrating what Aristotle later does in his definitional hierarchies.

West’s translation at 12a4-5 seems unnecessarily confusing: “And yet you are no less younger than I am than you are wiser.” Part of the confusion arises from the apparent solecism “less younger”, though I don't think that is what West actually means. Socrates is apparently presenting a proportionality, using a dative of the degree of difference: “you are younger than I am by more than you are wiser” (καὶ μὴν νεώτερός γέ μου εἶ οὐκ ἔλαττον ἢ ὅσῳ σοφώτερος· — i.e., “you are much younger than I am than you are wiser”). To me, the alternative reading from B (ἐλάττονι) expresses this more clearly. Still, is Socrates really talking about Euthyphro’s age (the point of the main clause), or is he slyly deprecating his wisdom? I understand it ultimately to mean “you're not so much wiser [than I] as you are younger than I." Given that age and wisdom are at least conventionally correlated, this seems a double put-down of Euthyphro.