Andromeda is the drop-dead gorgeous princess whom Perseus rescues from Cetus the sea monster. We don't get to hear much about her personality or anything in the story. She's not really much more than a pretty face, but that face is pretty enough to make Perseus kill a monster.
Andromeda is a fitting wife for Perseus, a heroic son of Zeus. Applicants for the position of Wife of a Greek Hero generally must meet two qualifications:
Well, everything seems to be in order. Application accepted.
For modern readers, Andromeda can bet a bit… well… disappointing. She's just a passive damsel in distress, a reward for Perseus' heroic deeds. We suppose that reflects the ancient time period the story comes from, but maybe you were still hoping for more.
One interesting way to look at Andromeda is to compare her to Psyche, Cupid's beloved wife. In some ways, these women have very similar stories. Both are so beautiful that goddesses get upset. In the case of Psyche, her good looks really irk Venus /aphrodite-venus/, the goddess of love and beauty. Psyche's parents also abandon their daughter to be eaten by a monster, but then her story becomes different.
The cool thing about Psyche is that she's the hero of her story. She falls in love with Cupid, looses him, and then fights hard to get him back. It's Cupid who is her reward. Andromeda, in comparison, isn't the star of the show. She's not the hero of the myth. Heck, we're not even sure if she loves Perseus. Or if, given the choice, she'd choose to marry Perseus or Phineus. (Though we suppose the choice isn't that complicated. Marrying your uncle is gross.)
If you want to read more about Andromeda, head over to "Themes: Women and Femininity."