This is a simple question with a somewhat complex answer, so I put together a presentation that covers it, drawing on the history of WordPress, what web hosting really amounts to, and comparing the different features of WordPress.com against some key features of WordPress.org.
What’s the difference between WordPress.org and WordPress.com?
Here is the difference in a nutshell: WordPress.com is a service that hosts WordPress blogs. WordPress.org is a community where people work on the open source WordPress software, which can be downloaded and run on your own web server. To see more information, you can download the slides for the presentation (pdf).