This expression is a metaphor that compares the idea of a car running without gas in the tank to a person who is still active while being tired or hungry.

If you are exhausted, tired, but still going, you are "running on empty". When the gas needle in a car points to "empty", there is still some fuel left, but not much. "I've been working since 6:00 this morning, 12 hours total, but we need to get this done tonight. I'm just running on empty right now."

The gas gauge says the tank is empty but the motor is still running. And there you sit; hoping you make it to your destination before the gauge tells the truth about how much gas you've got left. Jackson Browne sang the song, it's a classic, watch it on YouTube. And the movie (same name) which you can check out on IMDB. The leader of Libya is running on empty, we are surprised he is still alive. She is living on nothing but popcorn and Coca-Cola... she is running on empty. The American economy cannot support endless wars in foreign countries... the economy will collapse... maybe America is running on empty?