Why patients wear a hat for surgery?

I'm assuming you're referring to one of those hats which are almost like hairnets, which normally co-ordinate with the scrubs. The use of these hats on patients during surgery is actually fairly arbitrary - if it's a long operation and/or the patient has long hair, they are sometimes used just to maintain tidiness of their hair. However for the vast majority of operations, a patient will not find themselves wearing one.