Stopover programs enable connecting flyers to take a break in their flight itinerary for days or sometimes weeks. They are especially popular with airlines that serve a high proportion of one-stop international flyers.
Airlines often team up with local hotels, tour operators and attractions on cross-promotions related to their stopover programs, which they market as an opportunity to visit two distant destinations on one fare.
I know that is why Icelandic Air was created, and I think it is why a lot of the Arab ones were as well.