A starving artist is someone who sacrifices their health and well-being (mental and physical), as well as their material goods so that they can focus entirely on their craft.
Ernest Hemingway wrote,
"You got very hungry when you did not eat enough in Paris because all the bakery shops had such good things in the windows and people ate outside at tables on the sidewalk so that you save and smelled the food..."
"...Hunger is good discipline and you learn from it."