Automattic is a company that is strongly associated with a variety of open source software, particularly WordPress. While WordPress is not owned by Automattic (or anybody else), many of the core developers of WordPress work at Automattic, including its CEO Matt Mullenweg. Automattic develops many of the most popular plugins for WordPress including Akismet, Jetpack and WooCommerce. They are also custodians of the wordpress.com website, a service you can sign up for to host a WordPress website.
You can read more about Automattic at their about page.