What does a qualifying flight mean when referring to tier qualification?

A ‘qualifying flight’ is a flight from origin to destination, either on Emirates, flydubai or a codeshare flight marketed by Emirates but operated by another airline.

Your origin is the airport where you start your journey, and your destination is the final airport where you complete your journey. So a qualifying flight could be a complete inbound or outbound journey, or a one-way flight. Stopovers are not counted as a destination.