Analysis: Writing Style
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. Check it out:
And just as a sharp light will startle us
from sleep because of the spirit of eyesight
races to meet the brightness that proceeds
from layer to layer in the eye, and he
who wakens is confused by what he sees,
awaking suddenly, and knows no thing
until his judgment helps him; even so
did Beatrice dispel, with her eyes' rays,
which shone more than a thousand miles, the chaff
from my eyes: I saw better than I had
before: (Par. XXVI, 70-80)
Yikes. This is not to say that Dante is boring... but you do need to take the time to unpack his dense words.