PLEASE NOTE: Questions about wordpress.com use, account, setup, features, and support are off-topic for this site.
WordPress.com is a hosted blogging service that runs on the WordPress platform. This means that you don't have to worry about technical issues (setup, upgrades, backups, scalability, ...), but you get less customization options: a limited number of plugins and themes, no ability to run custom PHP code, etc.
WordPress.org is the home of the software itself. It is an open source project, which means that you are free to use and modify it. You have more flexibility, but more responsibilities too.
For more about the differences you can read "WordPress.com vs. WordPress.org".