Learn Spanish (Latin America): El crítico trata de explicar de qué se trata el arte moderno. - The critic tries to explain what modern art is about.

This sentence perfectly shows the difference between the two verbs! Tratar de means 'to try to' do something when followed by an infinitive like explicar. Tratarse de means 'to be about'. So, the critic tries (trata de) to explain what modern art is about (se trata).

I thought tratarse de was impersonal, so why does it have el arte moderno as a subject here?

You have a good memory! In strict traditional grammar, tratarse de is only impersonal, meaning it never takes a subject (like 'it is a matter of'). However, in everyday Latin American Spanish, it is incredibly common to use tratarse de with a specific subject to say what a book, movie, or concept is about. While a strict textbook might prefer de qué trata el arte moderno without the pronoun, using se trata here sounds completely natural to most native speakers.

Why is the de placed before qué in de qué se trata?

In Spanish, prepositions must always go immediately before the question word or relative pronoun they belong to. You can never leave a preposition at the end of a sentence like we do in English ('what modern art is about'). Since the verb phrase is tratarse de, the de must be placed at the front of the clause, giving us de qué se trata.