In very basic terms, a comedy in Dante's time was the name given to a work that started badly but ended well. If we examine The Divine Comedy, we will see that it falls perfectly into this category.

When the Comedy begins, in Inferno, Dante the pilgrim is in the middle of a dark wood, having wandered from the straight path. Before long, his way is blocked by three fearsome creatures: a wolf, a lion, and a leopard. Things really couldn't be much worse for Dante at this point.

But fast forward to the very end of the Comedy, in Paradiso, and Dante, having reached the final stage of his remarkable journey, comes face to face with God in the form of three circles, each representing a person of the Trinity: Father, Son, and Holy Spirit. What started off in the worst possible way for Dante has culminated in a vision of the Almighty. This is what makes Dante's epic poem both divine and a comedy.

One should also bear in mind that comedy in Dante's time was written in a low style. Much of the Comedy is indeed written in such a style, far removed from the elevated Latin traditionally used for serious subjects. Dante wrote his masterwork in the vernacular, in the Florentine dialect, which would've alerted his readers to the fact that his epic poem was a comedy and not a tragedy as those terms were commonly understood at that time.

In the broadest sense, all literary works can be placed into one of two categories: comedy or tragedy. A comedy has a happy ending, meaning that the protagonist doesn't die or suffer a crushing blow from which he can't bounce back. In a tragedy, the protagonist does die (or suffer a horrible fate, as when Oedipus blinds himself and accepts exile).

The Divine Comedy is called a comedy because it has a happy ending. At the beginning of the poem, the thirty-five-year-old Dante is lost spiritually. Halfway through life, his faith is draining away, and he feels as if he is stumbling around in dark woods. Beatrice, the Virgin Mary, and St. Lucia are concerned for him. They arrange for him to tour hell, purgatory, and heaven with the hopes this knowledge will set back on the straight path of faith.

This is a long journey, and Dante has much to learn, but in the end, Dante's heart has been fully transformed. He is able to ascend to heaven and into the Empyrean, where he sees God. This fills him with an overflow of love and wisdom that saves him from eternal ruin. Thus, this is a comedy: it has the happiest of endings for the protagonist.

The lesson, too, is that Dante is an everyman (or woman) figure. Redemption is possible for all humans if they follow the Christian path of virtue, faith, love, and hope.

The previous post was dead on.  The work is not very funny.  Although, I do find it humorous that Dante used his depiction of hell to place individuals whom he didn't like in the different levels.  If we were back in Florence of the time period, there would be much in way of satire in the work.  The harmony, unity, and symmetry that is presented at the end of Dante's work is where the comedy is present.  It is comedy in the sense of a vision where tragedy is absent.  Comedy, in this light, becomes the adversary of tragedy.  There are some works that seek to be comedic in nature, yet the tragic elements in their presentation can be isolated and bring some level of ominous shadow to the comedy presented.  This is not the case with Dante.  Even the most tenacious reading of it can reveal a comedic ending with God fusing all oppositions, embodied in the love of Beatrice.  Dante's work is called "the divine comedy" because it accomplished what it set out to do in terms of giving meaning to the religious pilgrim wondering how to account for the "lost" nature of mankind.  In this light, it is comedic because of its unifying and harmonious vision presented and in light of the notable absence of tragedy in its resolution.

This is a great question, deechavez!  We commonly assume that the literary terms COMEDY and TRAGEDY have to do with whether what happens in the work is funny or sad.  However, these terms are traditionally meant to tell the reader what they can expect about the structure of the work rather than being descriptive so much of the contents.

This isn't to say that you definitely won't find comic events in a work of literature called a COMEDY, just that it isn't necessary.

Dante's Divine Comedy is called a COMEDY because he conformed to two requirements of this structure:

1. It has a happy ending.  This, throughout works of literature, is the basic definition of a COMEDY.  Look for it in Shakespeare and other writers too.
2. The tone of the writing is in a LOW rather than HIGH style.  Dante was actually very original here, writing a poem about the salvation of Mankind, but doing it in an everyday language.

So, the next time you go to the movies to see your favorite comedy, see if it stands up to this structural definition of COMEDY.  Does it have a happy ending?  Is its language everyday (even sometimes vulgar)  in tone?