to hand something to a strong man for opening or to be moved. It implies that men are strong. It is most often used by a female to get something done that she isn't able to do herself, although has been used by smaller men to solicite help from larger, stronger men.
women might say:
Hey, could you man this open for me?
Could you man this over there for me?
a man might say to another man:
Could you help me man this over there?
(especially if it were too heavy for one person)