To give some concrete examples, if I wanted to fly United award travel SFO-LHR, I might want to choose SFO-ORD-LHR, SFO-IAD-LHR, or even SFO-LAX-LHR....
- In order to get award inventory availability if the SFO-LHR non-stop doesn't have any availability.
- To give me access to flights at different, perhaps better times of the day for my travel plans. There are only two SFO-LHR flights per day, but lots more different possible departure/arrival times made possible by looking at the connections.
- To give me access to different aircraft types. (In this specific example, United 767-300 aircraft with the new FC/Biz cabins are flying the IAD-LHR route, whereas no United 777-200 aircraft flying the non-stop SFO-LHR route will get new FC/Biz cabins anytime soon.)
- To let me disembark and stretch my legs.
- To gain access to the international gateway departure lounge at the connecting airport, esp. when that's a International First Class lounge that can be a rather nice place to take a break and enjoy some decent food.