The Trip Taken On The Way To Somewhere Else

Any journey with a change in it contains a potential short break. Turning a connection into two nights costs very little extra travelling, and the constraint is usually ticketing rather than geography.

The travel is already being done

The expensive part of a short trip, in time and money, is getting to the destination and back. On a journey that was happening anyway, that cost is already committed.

Stopping in the connecting city adds only the accommodation and the days themselves. Compared with arranging the same two nights as a separate trip, the saving is most of the journey.

It also removes the worst part of a connection, which is several hours in a terminal that count as travel time and produce nothing.

Fare rules decide whether it is possible

A single through ticket usually assumes continuous travel, and breaking the journey may or may not be permitted depending on the fare's conditions.

Where it is not, the alternative is two separate tickets, which costs more and separates the legs contractually. Whether that is worth it depends on the gap between the two prices.

Rail fares often handle this better than air fares, since break of journey is a long-standing concept in rail ticketing and is permitted on many fare types outright.

Some carriers sell the stop deliberately

Airlines with a hub have an incentive to encourage visitors to that hub, and several offer an extended stop at no additional fare as a result.

The terms vary and change, so the airline's own current conditions are the thing to check rather than a general impression of what is usually allowed.

The offer exists because the airline is competing for connecting traffic that could route through a rival hub. Giving away the stop is cheaper than discounting the fare.

Which cities this makes available

The value is that it opens destinations chosen by the route rather than by preference. A connecting city is rarely one that would have been picked deliberately, which is most of the appeal.

It also tends to produce places at the right scale, since hubs and interchanges are often mid-sized cities with more in them than their reputation suggests.

What it costs when things go wrong

Breaking a journey deliberately introduces the same risk as any split booking. A missed second leg is not the carrier's problem in the way a missed connection would have been.

The mitigation is to leave the second leg well clear of any tight timing and to treat the stop as a separate departure rather than as a continuation of the first journey.