WordPress is a free blogging platform that is built on open source (free, supported by a community of developers) software.
WordPress is a popular choice among bloggers as it is easy to use, includes a nearly infinite number of themes or templates - both free and at a small cost - and plug-ins (utilities that help you perform tasks within your blog), and is considered to be very SEO-friendly (search engines like it).
WordPress.com is a site where you can host a Wordpress blog for free. Your blog will reside on Wordpress' servers (such as yourblog.wordpress.com).
You can also host a WordPress blog on your own domain and server (such as yourblog.com). WordPress.org is the site where you can get more information on downloading and installing the necessary software and where you can get support information for your blog.
WordPress blogs are popular as they are considered both user-friendly and search engine friendly.