Empty leg is defined as flight from A to B where the aircraft is empty. Normally because we have to pick up passengers at another location then where the aircraft is located. It can also be because we have delivered passers at their destination and then fly back to the aircraft home base.
Empty leg can be sold at a lower price, but you have to adopt to other peoples schedule, in that way you can save 20-50% of the normal cost.
If the client that booked the flight in the first place, changes their schedule, you might have to change your schedule too.
If the main client cancel their flight, you can expect an higher price or to cancel and look for another empty leg.