Template overrides allows a user of your module to customize the view to suit their needs. A template override basically tells your Joomla! site to load a file from your site templates folder, instead of wherever it is normally loading from, and it effectively overrides the original code with your own code. You end up with two copies of the file: the original file that you don't touch, and your new version of this file which is actually used by your site. This way you can make whatever customizations you like including adding new features, or removing or hiding the ones you don't want.
When customizing a module someone else has developed, it is much better to use a template override than to hack the code of the module, because any changes will be lost when the module is upgraded if you edit the code directly. In case you have never been told this, you should never ever change a core Joomla! file; if you really need to change something, then override it. You wouldn't normally...