It seems like many are confused about what WordPress really is. So, putting it in a very simplest word – It is a FREE SOFTWARE that will help you create beautiful websites (example, this site, Heyletslearnsomething.com). There is no cost in downloading this software and it can be easily done via the official website.
How it works? WordPress needs to be installed on a server (or Hosting Provider), and your domain should be pointing to that that host. You can then install themes and customize as much as you like. As mentioned earlier, it is absolutely free, open source and provides regular updates, the only costing that will involve is on purchasing hosting or domain name (which is different). You can even setup the installation using a local server in your computer for website testing purposes (no cost involved).