Hermia affirms her love for Lysander by swearing on two symbols from ancient mythology.

 

First she swears on doves which are often portrayed pulling the chariot of Venus, the goddess of love and beauty. Because doves mate for life, they represent lifelong marriage and sexual fidelity.

 

Then Hermia swears “by that fire which burned the Carthage queen“

 

This is an allusion to a mythological story related to the Trojan war which supposedly took place around 3000 years ago. Most of Shakespeare’s audience would have been familiar with this story. 

 

The story recounts how Prince Aeneas of Troy, after his city was sacked by the Greeks …  made his way to North Africa … where he seduced Queen Dido, ruler of Carthage.

 

Queen Dido fell in love with Aeneas. But Aeneas believed that he was destined for greater adventures elsewhere, and soon abandoned Dido. After watching him sail away, the broken-hearted queen threw herself onto a burning funeral pyre.