The same core WordPress software is deployed in two very different ways through WordPress.com and WordPress.org.
WordPress.com is both a website and a business. You can create a free account on WordPress.com and have access to a hosted version of WordPress on which you can create a website. With a hosted version, the hosting company takes responsibility for maintaining the server and WordPress installation, relieving you of that burden so you can solely create useful content.
WordPress.com makes money by charging for feature upgrades. For example, if you want to use your own domain name on a WordPress.com site, there is a small fee to do so. There are also many companies that pay WordPress.com to host very large WordPress installations, such as BBC America, The New Yorker Magazine, and the official Star Wars Blog.
Because WordPress.com has to support many different sizes and types of sites, they are fairly restrictive when it comes to customizing individual sites. There are only a fixed number of themes(site templates) that determine the look-and-feel of their sites, as well as a small number of plugins(software modules) that provide different types of functionality.
WordPress.org is the official website for self-hosted WordPress installations. Self hosting means that you have downloaded a copy of the WordPress software and installed it on a server, which is a computer with special software that lets you serve websites and other data to users through the internet. This server could be an old PC in your basement (which is not really recommended) or in a high-tech data center. It’s up to you. A self-hosted installation of WordPress enables you to create a website that you fully own and control, and you are completely responsible for configuring and maintaining the WordPress installation.