The Maintenance module does one simple function, it deletes the Smarty compiled files in the templates_c folder. This is simply a convenient and easy way to do this instead of having to use an ftp client or your web host control panel to clear this folder out.
The reason that you may want to clear the template_c folder is if you have made changes to any of your templates, but they don't seem to take affect. Smarty will use the compiled template files in this folder and sometimes this will not show your changes. By clearing out these files, your changes will then take affect.
This does not change your site and doesn't have any ill affects on your site. This folder is a cache folder of sorts. Each time that the Smarty system renders a page it stores that file in this folder. It does this to help the speed of your pages being served.