What is the meaning of the phrase "a man of the world"?

The name of one of the Ernest Hemingway's short stories is "A man of the world". It seems to me that I understand the meaning of this phrase out from the context of the short story. But all the same it seems a little vague to me due to the fact that this seems to be an idiom with its own specific meaning. All the meanings of this idiom which I managed to google don't seem to fit in full for the name of the short story.

Could you help me to grasp the meaning of the idiom in this short story?

Edited (added):

"A Man of the World" Summary (from http://www.bookrags.com/studyguide-ernest-hemingway/chapanal059.html )

Blindy is a blind man that wanders among the local bars playing slot machines. He smells very bad and has a difficult time finding someone to give him a ride between bars. His favorite bar is the Pilot, where he gets along well with the bartender. The bartender explains how Blindy became blind. During a fight, his eyes were gouged out and then bitten off by his opponent, Willis Sawyer. Blindy, who refuses to be called by his previous nickname, Blacky, is content with his life and pities Willis Sawyer.....

I use a man of world to mean a person who is experienced in the ways of sophisticated society, which is the same meaning that the Italian un uomo di mondo has (one is the literal translation of the other).

We use A man of the world as a way to describe a person with broad work and life experience. They've seen and done many things and have a great deal of worldly experience.

I've heard it used with a slightly negative sense (in the same sense as "wordly") to mean materialistic, shallow or immoral (This is an older meaning, probably originally from the Bible, where "the world" is sometimes used to refer to the evil in the world, in contrast to the goodness of God and spiritual things).

I suspect Hemingway knew this meaning, though the more common meaning these days may also have been popular when he wrote (the more positive "broad work and life experience" or "sophisticated" meaning mentioned by others).