The proverb means that when the husband is good at being a man, the wife will tends to follow his authority and not challenge him all the time, even if she was known for being suborn or hard to handle. It emphasises the importance of masculine responsibility and authority in a relationship. When those are in place with the husband, the union tend to be a successful and prosperous one.
The proverb can also used to imply that if the husband treats his wife well, she will treat him well in return.
The origin of the proverb is unclear. It is thought to have originated in England in the 16th century.