Human Reason
Most Dante scholars agree that Virgil represents human rationality in the Divine Comedy.  Amidst a world that is constantly new, changing, and terrifying, the comforting voice of reason explains everything to Dante the pilgrim and the reader.  He describes the geography of the place, why sinners are punished according to their sins, why we see what we do - in short, Virgil always provides the reason why things are the way they are.  This is essentially the role of rationality in a philosophic sense of the world.  As we know, Dante was a student of philosophy, so he was well familiar with philosophers' tools to explain the world.  Virgil therefore symbolizes human reason in a very didactic sense.

A Torn Dante Dante was a great thinker, and he lived in a world with very conflicting ideas about science, religion, and literature.  For example, by 1300 or so, scientists knew that the earth revolved around the sun, and that the southern hemisphere was not just water.  And yet, people still clung to their old ideas long after they had been proven scientifically false.  The Divine Comedy was a hugely popular book, even after its publishing, despite the fact that it was framed by a system of physics which was essentially the same as Aristotle's.

Aristotelian Universe

Dante was faced with a real intellectual problem, and we can see how Virgil's presence in the Divine Comedy highlights it.  Dante is simultaneously fascinated with the ancient world, especially Rome, and he is also a firm believer in Catholic doctrine.  He was torn between the classical pagan world, so rich with the poetry of Virgil, Ovid, and Homer, and the transcendence and revelation of Christianity.  That a non-Christian, pagan world had produced the masterpieces of poetry (Aeneid, Iliad) that he was so enamored with was a big conflict for Dante.

Solution: Virgil
Viewed in this frame of reference, then, we can see that Dante's placement of Virgil in the Divine Comedy reflects his struggle to reconcile these two views.  First, Virgil's separation from Paradiso is absolutely essential.  That Virgil doesn't accompany Dante into heaven shows that Dante the writer believes that his two views must be kept separate.  Classical reason, symbolized in Virgil, has no place in the revelation of Christianity and must remain autonomous.  Dante hopes to avoid the conflict by keeping the two separate in his mind - as separate as Virgil and Beatrice are from one another.

Virgil - A Christian?
Virgil also represents the best bridge between Dante's conflicting ideas of classicism and Christianity.  In his 4th Eclogue, Virgil wrote of the coming of a little boy who would restore order and bring about happiness.  In hindsight, it is eerily reminiscent of the story of Christ, but there is no way Virgil could have known about Jesus at the time of his writing.  The 4th Eclogue has intrigued scholars for centuries, and Dante was no different.  Virgil's message was prophetic, he thought, which made him the most "Christian" of the pagans.  Virgil, as a pagan poet possibly predicting Christ's birth, represented for Dante the closest link between his conflicting fascinations with Christianity and classicism.