There are two ways to remove a category from showing up on your WordPress Theme’s Home Page: (1) You could dive into your theme’s functions.php file, or (2) You could install a really simple free plugin that will do this for you.
Method #1: Functions.php
This is not terribly difficult to do, but will require some very basic knowledge of working on the code in WordPress.
First of all, you’ll need to borrow some code. I found someone had written out the code here. Copy and paste that into your theme’s functions.php file and viola! You’re done.
Method #2: Plugin
If you are terrified of code and think you might mess up your site by using the first method, you can also keep a category from displaing on your WordPress theme’s home page by using this simple plugin.
Once you install the plugin, just go to your dashboard > Posts > Categories. Find the category you want to remove and click the box that says to remove it from the main loop.