Boccaccio, Petrarch, and Dante were the three vital components of the "common man" Italian literature of the pre-Renaissance, late Medieval Period. Of course of those three gentlemen it is Dante who is remembered the strongest, almost exclusively because of his Divine Comedy. Here are the reasons that Dante and his epic poem have stood the test of time.
1. The idea of writing literature that one's fellow countrymen can read, understand, and enjoy. This was a large step of forward progress in Dante's age, when few institutions, especially literature, were not democratized for the common man. Dante is able to accomplish this through the informal language of the poem and the fact that the work's original language was in Italian, rather than Latin.
2. The rhyme scheme of the work, which is done in the terza rima style. Terza rima's rhyme scheme goes aba bcb cdc ded, etc. The fact that Dante is able to keep this scheme up through the 14,000 lines of the entire work shows a master of poetry at work. Though this rhyme scheme is rarely preserved in English translations of the work, keeping it in mind as an English reader is still important.
3. The imagery Dante presents. The vivid imagery of hell's enormous sufferings and lamentations as well as the horrid, ghastly landscapes of the underworld in "Inferno" and later of purgatory and heaven will leave a strong impression on the reader.
4. The allegory of The Divine Comedy, which can be applied both religiously or spiritually. Dante's quest through hell, rise through the mountain of purgatory, and into the Kingdom of Heaven can represent to religious folks the journey of men and women to reach God. Or if you prefer a less religious perspective, the work shows that in order to achieve happiness and fulfillment, one must face the misery, the hopelessness, the terror, the disgust, and the depravity of the dark sides of life.
5. Vivid depictions of both Classical figures of Greece and Rome and of 11th-12th Century political and religious figures of Northern Italy. One is able, in reading this, to learn a good deal about Classical history and mythology and also of the political and social conditions of Florence and its surrounding areas (at least from Dante's perspective).
6. The commentary on sin/redemption and good/evil. While outdated and rather fascist by today's standards, the work presents clear-cut moral concepts and though merciless in its treatment of sin and unwavering in its support of those who follow God, it still through the voice of Dante's character in the poem, provides within its own rigid moral framework, a fascinating commentary on the laws of good and evil. An example of this is in the case of Francesca da Ramini and her lover Paolo who appear in "Inferno" in Canto V. Though Dante punishes them in hell for their adultery, his character in the poem does feel sorrow for them and empathy for their plight. So even if Dante is still condemning the sin, he still in his own way, provides commentary on the nature of sins. In "Paradiso" Dante inversely provides commentary on the nature of doing good and following God.
7. Theological and aesthetic value. The work holds a theological importance in the sense that it provides commentary on the nature of the Judeo-Christian afterlife. Aesthetically, it holds a good amount of merit because it is artful in its composition (material sense of aesthetic pleasure) and manages to reach deep within the soul with its horrific imagery ("Inferno") and heavenly imagery ("Paradiso"). (This represents the spiritual side of its aesthetic value).
8. Insights into the life of a fantastic author. While people may be hesitant to learn about the life of Dante Alighieri specifically, the poem I believe, in its display of Dante's psyche shows something of the souls of all poets. Especially with The Divine Comedy we get this feeling as Dante is not only the writer, but the central character of the work. So it is not only is his stylistic conceits that we get a portrait of Dante.
9. Geometry of the writing. Each line contains eleven syllables (hendecasyllabic) throughout and is also divided into three parts, like the holy trinity. In the end, the three heads of Satan gnaw upon the spirits of Brutus, Cassius, and Judas Iscariot, representing again a sort of trinity, this time an inverted one of evil. Dante uses the numbers and quantities of things both within the writing itself and in its composition to create meaning.
10. The idea of proportional punishments in hell and proportional rewards in heaven. The nine circles proposes an interesting concept, that people in hell are punished specifically for the sin that they are guilty of and vice versa in paradise. It is not only an interesting idea, but one, that for a good deal of believers, may have a degree of validity. The punishments that Dante creates for his sinners in hell and the rewards he creates in heaven are also interesting to read about.