There are actually many reasons to have square windows, but just one for having round windows—square corners in a pressurized cabin lead to stress concentrators that act like cuts which can compromise the structural integrity of the fuselage. There are many solutions to the problem of stress concentration, but rounding the corners of the windows is the simplest.

At any given moment, an airliner in flight is subjected to a wide variety of forces acting upon its various surfaces, from outside (aerodynamic loads) and from inside (pressurization). All these loads create stresses within the airliner’s structure, and as engineers know, sharp corners in a stressed surface tend to concentrate these stresses, making failure more likely. That is why engineers typically avoid putting sharp corners in stressed objects.

If you drive a car, observe that all vehicle windows have rounded corners. Similarly, the windows in your home also have rounded corners, not because of structural concerns but because sharp corners are much more prone to breakage.