Jung - Anima and Animus
From the way I understand it, everyone, male or female has both masculine and feminine personalities and it is up to the subjects whether they recognise that or not and to what level.  The idea is that in order to become all you can be you need to integrate yourself with your inner opposite sex.

The animus within the woman and the anima within the man are the opposing personalities to their sex and how they are 'supposed' to behave.  An example would be that if a man has a strongly developed anima (fully accepted and integrated into his psyche) the man will be fully open to emotionality.

The article from Wikipedia and this good article from Psychology Today may help.