"No woman No cry" contrary to social belief is about telling a woman that she shouldn't cry. The idea that we have about a man not crying if he doesn't have a woman,or the famous one "if a man doesn't have a woman he doesn't have reason to cry,because he doesn't have a woman to cause him pain(emotionally) or to stress him out".
Many people taught that's what it meant. But really and truly its only saying that women shouldn't cry because of hardships.
And also the woman in the song specifically:In the song the man is a travelling minstrel telling his woman he will come back for her.
"So dry your eyes I say, and while I'm gone
everything is going to be alright
everything is going to be alright now
no woman no cry, no woman no cry".