The windows in the airplane till the 1950s used to be square in shape. But after two planes literally fell apart mid-flight, the design flaw was quickly identified and fixed.
BOAC Flight 781after suffering explosive decompression crashed into the Mediterranean killing all 35 people on board and South African Airways Flight 201 disintegrated in the night sky at around 35,000 feet (11,000 m), killing everyone (21 people) on board. An extensive investigation was conducted on both crashes.The findings of the investigation proved that the mid air disintegration was due to their square windows.Any corners in the fuselage of an airplane become weak spots that can potentially endanger the safety of the people on board
Square window sharp corners naturally concentrate more stress, which further gets weakened by the immense air pressure. Curved or round windows distribute the stress of the outside pressure of air, and thus are stronger and prone to deformation because of the pressure.
The problem is not only with squares or rectangles; any shape that has corners in it is a potential danger to the safety of the airplane. This is the reason that curve-cornered windows are so common in commercial and private jets; they efficiently distribute the stress that they experience to a much larger area, which significantly reduces the chances of their breaking.
So, now that you know the real reason behind airplanes having round windows.