It means to be the foundation of the relationship. Not a substitute for God or some kind of taskmaster who bosses women around, but the backbone... somebody who can be relied upon. It doesn't matter if the woman is weak and obsequious or if she's a drill sergeant who can kick a strongman's butt in a bar fight. To be the man in the relationship is to be there for your woman and/or family.
Browsing profiles on internet dating sites I have more than a few times seen a woman saying that she is looking for someone who will be "the man in the relationship".