Socrates asks Euthyphro to offer him a definition of piety or holiness. The purpose of establishing a clear definition is to provide a basis for Euthyphro to teach Socrates the answer to the question: "What is piety?" Ostensibly, the purpose of the dialogue is to provide Socrates with a definitive meaning of "piety", with which he can defend against the charge of impiety in the pending trial.
Socrates seeks a definition of "piety" that is a universal (universally true), against which all actions can be measured to determine whether or not the actions are pious. That, to be universal, the definition of "piety" must express the essence of the thing defined (piety), and be defined in terms of genus, species, and the differentiae.
Hence, the Euthyphro dialogue is technically important for the dialectics of theology, ethics, epistemology, and metaphysics. Indeed, Plato's approach in this dialogue is anachronistic, because it is unlikely that Socrates was a master metaphysician; nonetheless, Aristotle's expositional treatment of metaphysics is rooted in the Platonic dialogues, especially in the Euthyphro.