There are a couple of different scenarios involving direct flights that even those who purport to know these things get confused:

• Flight travels from origin to stop(s) to final destination on the same aircraft and flight number;
• Flight travels from origin to stop(s) to final destination with a change of aircraft at one or more of the stops, on the same flight number.

Definitions of "direct":
From dictionary.com:
adjective

1. proceeding in a straight line or by the shortest course; straight; undeviating; not oblique: a direct route.

From Merriam-Webster's Dictionary:

Definition of direct

It goes back long before the airline industry even existed to the rail industry. Even the term change of gauge comes from them from when a train could only go so far as the next section of track was physically a diffrent size. Everyone would get off one train and move to a diffrent one. At the start of the aviation industry they had the same issues where certain planes could only fly parts of routes then you would need to switch planes to continue on. It was then used to create direct flights from cities without international service, aka Buffalo to London which was really a stop in JFK and a transfer to a new plane that was marketed as non-stop to London for NYC pax.