"A man's man" has qualities other men admire; he is a man other men would like to be, a man who enjoys activities which require physical as well as mental strength and stamina; however, the definition is not stuck in some macho paralysis as the qualities that make a man are changing and being revamped from time to time. John Wayne may have a man's man at one time, but for this day and age, he would be seen as too conformist and black and white in his views. Independence, integrity, self-sufficiency, ground-breaking vision, brave physically and morally, and loyal to other men to an ocassional fault are relevant qualties of a man's man.
"A man's man" will stand up for another man rather than cave to some dishonest demands of a close female; a man's man would do what's best for another guy without taking undue advantage, evidencing a certain nobility; a man's man doesn't always grin and bear it as honesty about one's limitations defines the character of a man and engenders the trust of other men. He withstands the peer pressure of women and other men when it is falsely leveraged against him.