An empty leg, or empty sector, is an unsold portion of a booked one-way private charter flight on a specific aircraft. Usually, an aircraft needs to fly empty back to position in for the next customer or return to its home base after a booked flight.
This repositioning flight is what we call an “empty leg”. For example, if an aircraft that is currently on the ground in Chicago, is booked for a flight from New York City to Boston, it will need to fly to New York City to collect the passengers and to start the flight. So the Chicago to New York City flight would be a potential empty leg. This infographic might help: