It means that you are not on a non-stop flight. And that you will stop someplace else, then you will have to get off that plane, and get on another plane (which is the connecting flight) and that plane will then get you to your destination. Sometimes, if you try to get real cheap fares, you might have 2 or 3 connecting flights.
For example: I live in New York and lets say I want to go to Dallas, Texas. If I have a flight that goes straight to Dallas, Texas then I have a non-stop.
But if my flight says it will first stop in Florida, then I have to get off in Florida and then "connect" get on a different flight, and then that flight goes to Dallas Texas, this new plane I just boarded is my "connecting flight".