It's inspired from literature. It means someone who views themselves as the main character of the world's story. In some literature, the world tends to revolve around the main character. (This is not true of much of literature that deals with, for example, character studies, but think of books like Ender's Game or Lord of the Rings.)
Although we are each usually the 'main character' of our own story, we typically know that we are not "the main character" of the world broadly. Some people act in ways that suggest they may not understand the difference. People refer to them as having "main character syndrome."
IMO the people that throw around phrases like narcissist, main character syndrome, lack of empathy, etc. usually know nothing about the person they are attempting to diagnose and simply have differing perspectives that they can't see eye to eye on.
