WordPress is a content management system (CMS) for websites and blogs. Edit content with a word processor-type interface, change how your site looks using themes, and add functionality with plugins.
WordPress.com is a hosted solution for personal sites. Easy to set up, a limited number of themes to choose from and no plugins allowed. WordPress.org is a self-hosted solution that allows use of any theme and plugin, but you pay for hosting and are responsible for maintaining your site. Which is best depends on what you need.