Does SharePoint 2013 provides any capabilities of having a Calendar inside my Sharepoint 2013 sites , where we can configured things such as events, public holidays, etc. and users can browser the calendar and see the per-defined public holidays and events?
Depends on what you mean.
Yes, SharePoint does have a list type (App) called Calendar which you can add to any site.
No, it doesn't include holidays.
But you can create one (or more) "global" calendar(s) like holidays, events, ... and then add them as Calendar overlays to the individual calendar on each site.
You might want to use something like SharePoint Holiday Loader to load the holidays