"The next is she who killed herself for love, And broke faith with the ashes of Sichaeus; Then Cleopatra the voluptuous."
"She who killed herself for love" is Dido, one of Aeneas' lovers. According to the Aeneid, she was the daughter of Belus, king of Tyre, and the wife of Phoenician Sichaeus. After her husband's death, she swore an oath to stay faithful to his memory and fled to Africa, where she founded the city of Carthage. However, she fell in love with Aeneas and turned her back on the oath she once swore. When Aeneas followed the gods' bidding and left for Italy, she committed suicide in desperation. This episode is recounted by Virgil in book 6 of the Aeneid - Dante has entirely followed him in his description.
Cleopatra (69-30 BC) was the daughter of Egytian king Ptolemy Auletes, famed for her great beauty and extraordinary intelligence: for example, she is said to have mastered at least six or seven different languages. She was beloved by Caesar, which helped solidify her grip on the throne. Her son Caesarion may have been fathered by Caesar. After Caesar was murdered, she became the lover of the general Mark Antony, one of the triumvirs ruling Rome. Together they planned to distance themselves from the Roman empire and seek independence; after losing a final naval battle against Octavian near Actium, they both committed suicide, she by letting an Egyptian cobra (asp) bite her.