"We can begin by observing that this is a new kind of writing," notes Martha Nussbaum about Plato's philosophical dialogues (The Fragility of Goodness , p. 122). She places Plato in a really interesting place, against Greek tragedy, his own earlier aspirations of tragic poetry, human vulnerability and control (tuche versus techne ), Socrates' lack of writings, and Aristotle's puzzlements at his teacher's dialogues.
What is interesting is her point that Plato has created his own genre for his philosophical thought. We often think of matching form and content as something very modern, but once again Plato beats us to it. His content demanded something different, and so he created a form all his own. Similarly, the Christian gospels have also defied easy categorization, being biography, history, revelation, religious teaching, and passion narratives in their own unusual ways (and unusual for their era, as was Plato).
Millennia later, we are still mulling over why Plato wrote in dialogues--why not poetry, tragic drama, or essays? We continue to delve into the place and role of tragic drama for philosophy and religion. Plato's genre, these parabolic philosophical dialogues, says something about his method and content, and his legacy is a genius that continues to goad us for answers and new ideas.