Window shutters are designed with two functions in mind. First of all, they help protect against the elements, especially wind, but they also provide privacy as well.
With respect to protecting against the elements, these days the only type of shutters that actually do this are hurricane shutters which are designed to protect windows.
Second, shutters are decorative. Of course, the decorative purpose stems from the functional purpose. Originally shutters were used in place of windows and so they were the only option for many homes to keep out the elements.
However, now it’s unthinkable to not have windows so other than privacy and hurricanes, shutters are decorative.