
Max M. answered 04/24/19
Harvard Literature major with 20 years of coaching writers
There are a lot of different versions of the mythology, but the basic idea that Shakespeare's audience would have understood is that Theseus and his army defeated the Amazons led by Hippolyta. Whether in so doing he earned her respect, or whether this is a forced marriage of a prisoner of war is a question open to your interpretation.
One possible way to think of Shakespeare's use of Greek mythology is to think of superheroes now--there's a given cast of characters, and basic story points that everyone is familiar with, but within that, you're free to tell your own stories. If you think of Theseus and Hippolyta as a bit like Batman and Catwoman, you'll be in the right ballpark.