There are two different sides to WordPress, so it is understandable when people are confused. Before sorting this out, allow me to explain what WordPress is.
There are many different content management systems (CMS) available for websites, one of which is WordPress. It is the most popular type of website in the world, and at the time of this writing the ones hosted on wordpress.com alone number 62,602,685, written in over 120 languages.
WordPress can be as complicated and powerful as you need it to be, from a blog to an e-commerce site and beyond. One of the things that makes WordPress different is that it is what is referred to as “open source.” This means that thousands of people all over the world are constantly contributing to making it better— adding features. fixing bugs, creating new plugins (plugins are mini-applications embedded within websites) and themes, and participating in an online help forum. Basic WordPress is free—only premium plugins and themes cost money.
Ok, so this brings us back to the original question. WordPress.com is completely free, both the website and the hosting. To a degree, this is a case of you get what you pay for. It is a terrific value in that they are providing the hosting and the security, and you don’t need to worry about backups. The down side is that, unless you pay extra, your URL will look like yourdomain.wordpress.com. There are also limitations to what you can do with it. No e-commerce or advertising like Adwords is allowed. You can’t add any plugins to supplement the generous collection provided. The themes available are limited, but they can be customized, and there are also a collection of premium plugins available. To put this in perspective, the New York Times, TED, CNN, and the National Football League are all wordpress.com sites, so they are nothing to sneeze at.
WordPress.org is the WordPress where your own domain name is a given, and anything goes—e-commerce, a LOT more customization, plugins for just about anything you can imagine and premium themes (which may or may not be superior to free themes. Generally speaking, it is better to have a wordpress.org site for a business.
To your business success!