An important question raised by Socrates' appeal to Euthyphro--to present a general standard by which all holy deeds can be recognized as holy--is how much Plato's Theory of Forms is present in this dialogue. The Theory, roughly stated, is that for every abstract idea (and arguably for material objects as well) there is a corresponding Form: the Form of Beauty, the Form of Justice, the Form of Courage, etc. Anything in the sensible world which has a certain quality only has that quality by virtue of its participating in the Form associated with that quality. While the sensible world is imperfect and perishable, the world of Forms is a transcendent reality of perfection and immortality. The goal of the philosopher, according to Plato's theory, is to properly understand and appreciate these Forms, freeing his soul from the mundane material world.
The Theory of Forms is best exemplified in Plato's great middle period dialogues, such as the Phaedo and the Republic. The early dialogues, among which the Euthyphro is counted, are centered around Socrates' teachings and do not yet deal with the Theory of Forms. Plato's theory is nevertheless present in this section, however. In asking Euthyphro to define holiness according to some standard common to all things holy, Plato is employing much of the vocabulary he would later use in his more explicit discussions of the Theory. Still, there is no reason that we should read the technical aspects of the Theory of Forms into this discussion, since Socrates' questioning makes sense even if we read it in an entirely non-technical manner. The Euthyphro is a paradigmatic early dialogue; it would be odd to ascribe Platonic theories to such a work.
We can easily see Socrates' conviction that true knowledge of a concept comes only when we can properly define it. That is, we cannot say we know what holiness is if, as Euthyphro does in this section, we only point to a few instances of things we consider holy. Rather, we must be able to give an overarching definition that will presumably help us to explain why particular instances of holiness count as such. It has been suggested that Plato, in later dialogues, will ultimately conclude that the Theory of Forms is the only way to provide satisfactory definitions. The Euthyphro and other early dialogues end at an impasse, where the interlocutor is made to realize that he does not understand what he claimed to know, but no positive definition is given. A Platonist might suggest that no positive definition can be given without the Theory of Forms.
The brief discussion regarding Euthyphro's literal treatment of the Greek myths may seem out of place here, but it will be brought back into the dialogue at a later time. It should be noted that Athenians at this time generally did not believe the myths to be literally true. Euthyphro's proud and dogmatic insistence that he does know the truth regarding these matters only makes him appear less credible. (His position might be compared in modern times to a religious fundamentalist.)