Why does Mac OS X requires repairing of permissions for maintenance while other OS (windows /Ubuntu) doesn't require it? Please explain briefly why repairing of permission is  one of the maintenance tool for mac os x exclusively .
Why it isn't done on windows?
Only because OS X offers a convenient way to repair permissions shouldn't be taken as an indicator that other operating systems don't need similar functionality as well. At least in the Linux world it depends on the distribution whether something similar is available and how it is run (e.g. periodically via cron).

As for the "why is this required in the first place": Software is usually not bug-free, neither are Installer applications. So permissions may get changed in unexpected ways over time. Having a function to repair them may save a lot of time wasted for hunting such issues down.