As the great wiki says:
Socratic dialogue (Ancient Greek: Σωκρατικὸς λόγος) is a genre of literary prose developed in Greece at the turn of the fourth century BC. It is preserved in the works of Plato and Xenophon. The discussion of moral and philosophical problems between two or more characters in a dialogue is an illustration of one version of the Socratic method. The dialogues are either dramatic or narrative and Socrates is often the main participant.
Note that Socrates is not necessarily a character in these--any dialogue in that style gets this tag.