Why the Aeneid is among the great books?

The Aeneid was the Roman national epic, and one reason why the Aeneid is an important book in world history is simply because Roman civilization was one of the most important early civilisations (especially for Europe).

Another reason for the Aeneid's importance is that it is the first modern epic poem. The Odyssey and the Iliad were written about mythical heroes, but they were also written during a semi-mythical period: Homer is writing about warriors who inhabit a world not very different from his own (or at least, this is how it would have seemed to the classical Greeks who relied on his poetry).

The Homeric epics are stories of heroic derring-do written at the time (or relatively near to it): much as if we had an account of the Gunfight at the OK Corral actually written by Wyatt Earp.

But the Aeneid is set in a time long, long ago, and far, far away (like a film about the Gunfight at the OK Corral made in 1996). The people who read the Aeneid knew that they were listening to a story, and a story told a long time after the events it describes. The Aeneid is fictional and literary in a way that the Odyssey and the Iliad are not.

The distinction is handled in some detail by Brooks Otis in his book: Vergil, A study in Civilized Poetry.