The work that you do for a living is the work that you do in order to earn the money that you need.

You use living when you are talking about the quality of people's daily lives.

You use living to talk about the places where people relax when they are not working.

The living are people who are alive, rather than people who have died.

If you say that someone scrapes a living or scratches a living, you mean that they manage to earn enough to live on, but it is very difficult. In American English, you say they scrape out a living or scratch out a living .