The shortest route between Chennai and Houston (for example) is a great-circle route, which takes a flight almost directly over the North Pole. A non-stop flight seeking to minimize mileage and fuel costs would take this route.
However, other factors often influence routing decisions.
Often flights are direct but not non-stop, meaning that the aircraft makes intermediate stops, even though passengers going directly from Chennai to Houston need not change aircraft. These intermediate stops may require a different routing from the theoretical great-circle route.
Traffic considerations may also alter the route. Over land especially, there may be airways that commercial flights are expected to follow in order to simplify traffic control. This may also be true over oceans.
Weather conditions are another factor. Prevailing winds are enormously important, and a longer route over the ground with tailwinds aloft at cruising altitude may be preferable to a shorter route over the ground with headwinds aloft. Storms must be avoided at all costs, also.
There are sometimes political considerations, as some countries may place restrictions on overflight of their territories.
Finally, some aircraft are restricted in the distance that they are allowed to fly from land, and may have to take a less direct route in order to stay closer to land masses. This is especially true for twin-engined aircraft. The reason for this restriction is that the aircraft must remain within flying range of land even after a single-engine failure. The fewer engines an aircraft has, the more vulnerable it is to a single-engine failure. Modern twins can fly for extended periods on just one engine, but they still have more restrictions on oceanic flight placed upon them than four-engined aircraft.