Would you call a train from A to B which has a few stops in between a 'direct' train? I most certainly would, for one.

Then why not an airplane? It's the same thing, it's just a transportation vehicle bringing you from A to B, usually non-stop but sometimes with some stops in between.

These flights are very common in Brazil, for example, where sometimes you have a non-stop option and a direct option with 2 or 3 stops at some airports between cities.
In Europe itself, these kinds of flights have become very rare. A famous one is BA from london city to JFK which has to stop in Shannon to refuel. But that's one of the few I can think of. The low cost carriers offer only point-to-point non stop flights, and the mainline carriers offer flights with a transfer point in their hub. I do not know of intra-european airlines who operate flights with stops, where you can book either part of the way or all of the way.

In the past, when we went to brazil the aircraft would go to Sao Paulo, then we had to wait a while and then it would continue on to GIG. I believe it was Varig, or maybe BA, I was quite little back then. Such 'tag ons' still occur a lot to these days but less than they used to.