I have created a new category in the backend.
But it is not automatically showing in front end.
Please check whether you have set the values of:
Description: Enables or disables the category
Description: Decides whether the category will be shown in the top menu or not.
Description: Decides whether the category will be shown in the layered navigation on the category page and search result page or not.
If you have set the above values correctly, then do the reindexing from System >> Index Management and flush Magento Cache from System >> Cache Management.
I hope it should solve your problem. If not, then you may be using a nonstandard theme which has some custom setting to show/hide category in the frontend.