In what ways is Dante's trip to hell an allegory?

Dante's Inferno is an allegory, which means it is a work that operates on both a literal and a symbolic level at once.
Take the first canto of Inferno, for example. Dante wakes to find himself in the "dark wood of error." His character is literally in a forest that has a path (the "straight path") and a hill in the distance. On the symbolic level, the forest represents a life of sin, while the path represents a path of redemption that takes the contrite and forgiven sinner to heaven (the hill). In this canto, Dante is also ambushed by three beasts, which represent temptations like greed, anger, and lust. He finds that he cannot continue on the path while those beasts are in his way; this symbolizes how Dante does not feel able to overcome his temptations yet. Luckily for him, Virgil appears and offers to take Dante on a journey through all of the circles of hell as an alternate way to purgatory and then to heaven.
During the journey, Dante witnesses the symbolic punishments of a variety of sinners. For example, the sinners who are in the second circle, for "the carnal," are swept up in a whirlwind for all eternity, like they were swept up in their emotions during their lives. Each circle of hell punishes the sinners therein in appropriate ways that reflect the sins for which they are being eternally damned. At the end of Inferno, Dante climbs onto Virgil's back and together they literally surmount Satan himself. The symbolism here is clear: Dante must overcome the most evil being of all to move away from a life of sin.