The backhaul check in airfares is about the following: when you travel from your origin city via another city to your final destination and this other city is farther away from your origin than your final destination, the chance exists that the airfare to that other city is more expensive than the fare to your destination. In airfare construction your initial fare is calculated between origin and destination. So you could 'cheat' the airline by buying a ticket from London to Hamburg via Berlin (Berlin is farther from London than Hamburg and the fare is probably more expensive). So when you leave the plane is Berlin, you have flown that at the fare London - Hamburg. However, the airlines do know this trick also, so they have devised the back-haul check (in full the One-Way Backhaul Check): If there is between your point of origin (London) and your final destination (Hamburg) a point in your itinerary with a higher fare (Berlin), than this higher fare must be charged. This rule applies only when you make a stopover (interruption of your journey of more than 24 hrs) in that intermediate city.