If you have your own hosting account, then you would need to install an instance of WordPress on it in order to use one of our themes. WordPress is free, and you would download it from
WordPress.org (or in some cases, hosting providers offer a 1-click install service). WordPress.com is their free blogging version of WordPress, and you would not be able to install our themes on one of those - you can read more about the differences
here. It's only those free blogging versions of the site which have the xxxx.wordpress.com URL, so you would not have to worry about that when installing it yourself. I hope this information helps. Thanks.