The History of WordPress
WordPress, created by Matt Mullenweg, was originally a blog posting site written in PHP, called b2. The site used PHP for its blog-like needs, then utilized MySQL to dynamically generate new pages, so they didn't have to be rebuilt every time a new page was needed. In 2003, b2 was in a pretty rough place, to where no one was maintaining the site, nor was fixing any security issues, and because of this, Matt and Mike, a close friend, decided to make a fork of b2. It initially focused on improving upon scripts to make better blogs, but it was also backed with the ideas of allowing others the freedom to make things.
After creating the fork, Matt focused more on the web standards of his site, and continued to prioritize the usability of WordPress and the simplicity of it. As time moved on, he continued to add more functionality and features to WordPress, as well as increasing the size of the development team that worked on it.
WordPress.org
WordPress.org is the organization that runs WordPress for individual users. Users that want to create a website can use WordPress absolutely free of charge. That being said, those that go through WordPress.org to get their installation of WordPress will need to use a hosting service to host their website with, as the WordPress software is completely open-source and free, but the hosting for the service is either hosted by you, or can be ran through WordPress.com.
WordPress.com
WordPress.com is the commercialized version of WordPress.org. While this site also uses the WordPress software, there are plans in place to also take care of hosting for you. In addition, WordPress.com provides plans that are better suited for smaller businesses and larger entities for reliability and ease of use. Costs range from a $4 per month personal plan, all the way to an enterprise plan starting at $25,000 a year.
Summary
WordPress was originally a fork of the blogging site b2, but due to the stopped support of b2, Matt decided to make a fork of b2 called WordPress, which transformed from a simple blogging site into the web content management system it is today. WordPress.org and WordPress.com are similar in the fact that the WordPress software is free to use, however the former requires self hosting and more technical work, while the latter offers a more commercialized approach, offering plan options for hosting and other quality of life features.