In addition to Dante's difficult 14th century Florentine dialect (which you miss altogether in translation), his text is written in meter. In other words, it's poetry – complete with a complex rhyme scheme and a definite rhythm. That's what we mean by "formal"; the text has a very specific form from which it never deviates. It also adheres to the epic genre, injecting its verses with invocations to the muses, epic similes, deus ex machina, and a laundry list of characters.
By "elevated," we mean that Dante speaks in challenging five-syllable words, never-ending sentences, and a rather stuffy tone. This is not to say that Dante is boring, if you take the time to unpack his dense words.