Interesting question. Mostly subjective I suppose but I would suggest that it's got to do with doing whats right regardless of who is looking and knowing when it is better to do what is good than to be right.
Keeping your head when others are losing theirs, acting like a leader when needed and a follower when it's best. To know when to be sensitive and to act accordingly, and to learn form your experiences so that in future you can accept the benefit of that lesson.
Caring for those who find themselves helpless, and standing up against those who would harm others to the detriment of all.
A man knows how to be exactly what he needs to be and has the sense to act accordingly.
What you are describing are all very positive and desirable qualities... But both men and women can, at least in my opinion, demonstrate these qualities. Why associate them to the male sex with the word 'manliness'? Doesn't it diminish the female sex by insinuating that someone who DOESN'T have these qualities is womanly?