Here is a little bit more background on the character of Anna:
"After Aeneas' narration, Dido had listened with growing unnatural love and desire for the stranger (a foreign prince destined to come by decree of an oracle).
The only person she could talk about this was to be her sister, Anna. Anna didn't realise the love was not natural; she was unaware the gods had inflicted upon sister a love that would bring tragic consequences to her queen. Anna thought that Aeneas would be the perfect husband for her sister, a fate that was not meant to be. She encouraged the queen to give the utmost attention to their suppliant and guest."
Anna is Dido's sister. She persuades Dido that an alliance with Aeneas is in her own best interests as well as in the best interests of Carthage.