This is a good question, especially in view of the Roman hatred for Carthage. For example, the archenemy of Rome in the Republic was Hannibal the great Carthaginian general. This fact must have struck a cord with the readers of Virgil's day.
In the Aeneid, as Aeneas and a small group of survivors are setting sail to found a new country, they unfortunately catch the notice the goddess, Juno. Juno hates Aeneas, because there was a prophecy that stated that the Romans would destroy her favorite city, Carthage. For this reason, she gathers the help of Aeolus, the god of the winds, and they create a storm to destroy the Trojans. Aeneas and his men are driven off course and under great hardships.
The storm is so big that the god, Neptune notices the storm and rebukes Aeolus for overstepping his boundaries. Neptune, therefore, calms the storm. There are seven ships left. Moreover, they set sail for the closest land they can see, which is the land of Carthage.
While they are in Carthage, Aeneas meets Dido, the queen of Carthage, and they fall in love. Aeneas is even tempted to stay, but his sense of piety or duty gets the better of him and he leaves.
Jupiter promises to give them an empire without end. "Imperium sine fine dedi."