True Manliness is a state of mind/way of life that isn't restricted by gender (I know some incredibly Manly women!).Macho-ism, and mating rituals aside, it's all about having the balls to live the way you want, and being able stand up to whatever gets in the way of that.
It's about having guts and confidence. Sure, there may be a little arrogance in the way of Manliness, but it's arrogance in cool way.
There's really no set definition to this view of manliness, and the points I've put are but a few of the ones I've discovered, but everyone has their own little journey to find out what it means for themselves. As much as I'd wish it to be otherwise, these values can be explained and described and told, but that means nothing unless you discover and experience them yourself.