A gold star hovering over a building indicates that it has been polished. To know when exactly someone polished a building (unfortunately not which though), just take a look at your event history. (Click your town hall, then 'News' and then 'Event History')
As for the duration of any polish, Balkana already answered that.
Regards,
Bloodwyn
P.S.: For the future, I recommend you use the search function in the top right corner of the forums.
Similar questions have been raised before. Take a look
here