The Euthyphro is primarily concerned with asking a Socratic question, “What is piety?” and working through arguments to arrive at a credible answer. There are however, several important and underlying arguments going on beneath the surface of the text. Plato has written this book in his usual dialectic fashion, which was also considered by himself and Socrates to be the only way at which philosophers could acquire knowledge and a soul good enough to commune with the Forms in death. The dialectic simply means question/answer format.
The major points to be highlighted in this text have already been discussed in the summary section, and they are: the essence criterion, the one over the many principle, and love of wisdom. The essence criterion is a feature of Platonic dialogues whereby he wants the answer to Socratic questions to reveal the true nature of whatever it is the characters are trying to learn about. For example, the essence of a chair is its “chairness”, or in other words not only its function (to be sat upon), but also its nature (whatever the nature of a chair may be). And Euthyphro has trouble giving the essence of piety because he instead gives examples or incorrect answers.
The ‘one over many principle’ is the theory behind Plato’s Forms which are presented and detailed in other dialogues (Phaedo, Republic, Meno, Parmenides, etc.). It simple means that a statue of Helen of Troy, for example, is considered beautiful because it participates in the Form of Beauty. And the Form of Beauty is an intangible, divine, perfect, immortal theory of the idea of beauty-much like a sort of heaven for Plato. There are many other forms (the Good, the True, etc.) and the forms give identity to all sensible objects in the world, as perceived by humans. There is one form of Beauty that reigns over all beautiful things.
The love of wisdom that Socrates has and illustrates in this dialogue is simply the love that a true philosopher must have if he is to work his way from ignorance to belief to true belief and finally to knowledge, which ultimately can only be arrived at in death. Plato greatly admired his predecessor and teacher Socrates and most of his dialogues depict Socrates in the best of ways, with a passion for the dialectic.