What is the "divided duty" that Desdemona talks about?

Desdemona says that she has divided duty or loyalties to both her father Brababantio. Now that she is a grown woman, her loyalties have switched to Othello. She points out that this was the same case with her mother who swore loyalty to Brabantio when she was married.

"I am hitherto your daughter, but this is my husband"