WordPress.com is a blog network run by Automattic. It uses WordPress software, but individual blogs are hosted and managed by WordPress.com. This is a free service with premium addons and upgrades.
Here at WordPress.org, you can download WordPress, the web software that WordPress.com runs on. Once you’ve downloaded it, you can upload it to a web server and run your own WordPress website.
There is useful information about this distinction on the WordPress.com website.
WordPress started out life as a fork of b2/cafelog by Matt Mullenweg and Mike Little. The first version was released in 2003
One of the principle advantages of WordPress is that you are in control. Unlike remote-hosted scripts such as Blogger and LiveJournal, you host WordPress on your own server. Installation is very simple, as is the configuration. Unlike other software programs, there are not a million files to chmod nor are there dozens of templates to edit just to get your site set up and looking the way you want.
Also, Blog pages in WordPress are generated on the fly whenever a page is requested, so you do not have multiple archive pages clogging up your web space. Waiting for pages to rebuild is a thing of the past because template changes are made in scant seconds.
WordPress is built following W3C standards for XHTML and CSS, ensuring that your site is more easily rendered across standards-compliant browsers. Other browsers are supported with a few hacks; it’s a reality of the web that hacks are necessary.
Aggregator support is built-in with a number of standard RSS configurations already done for you, as well as Atom. Following standards makes your WordPress site easier to manage, increases its longevity for future Internet technology adoption, and helps give your site the widest audience possible.