If you answered "A Hunger Artist," you're kind of right. If you answered "A Starvation Artist," you're also kind of right. Heck, if you said "A Fasting Artist," we wouldn't call you wrong either.
But the real title is "Ein Hungerkünstler."
Kafka wrote the story in German, so you're probably reading an English translation. Different translators, well, translate the title differently. "A Hunger Artist" is the most common English translation.
The title refers to the title character, an unnamed "hunger artist" (or "starvation artist," depending on your translation) who entertains crowds of people by sitting alone in a cage without eating for long periods of time. In the beginning, his act is very popular; by the end of the story, he dies, still fasting, virtually forgotten. By leaving the main character – actually all of the characters – unnamed, the story takes on the quality of a parable or an allegory.