Ok... I put "That is my woman." and it marked me incorrect. Can someone explain why? I thought "wife" was "manželka."
"Žena" can mean "wife" as well, in certain context - usually with a possessive pronoun like here. Slaves were never as popular as in the U.S. here, so "This is my woman." has never really made sense. :D
My translation was literal based on what I knew žena to mean from the lessons. In English, at least in slang/informal speech, endearing phrases like "my man" or "my woman/girl/lady" can mean things like "my friend, my boyfriend, my girlfriend, etc." (but usually not "my husband" or "my wife").
But it sounds like in Czech, or at least in this context, žena, can ONLY mean wife, which is good to know.
Yes, it can only mean wife (husband for a man). More or less every time you see my, his, her, your in front of woman or man it means husband or wife. There are some other situations when it would mean that but the possessive pronoun is a good bet.