WordPress is a blogging platform that can be installed on your server manually or using a wizard through your host. You download this software at wordpress.org and use their mega library of 3rd party plugins, themes and add-ons. Many are free with paid version options. You will need to have some basic webmaster skills to install. WordPress.com is the online hosted version. Keep in mind, you give up lots of customization options when going with a free hosted version. WordPress.com is great for beginners. You won’t be able to add sub-domains or install 3rd-party plugins. Positives are that you will have a hosted and updated blog with built-in SEO features and mobile users will have no problems viewing your site.
I personally prefer the self hosted WordPress platform. I own a reseller account and can install a new blog on a new domain in 15 minutes. I host WordPress blogs for myself, friends and family. If you purchase a re-seller account from a hosting site, you can be up and running with a new blog on a new domain in 15 minutes. With a self-hosted wordpress blog, the sky is the limit. It is very scaleable with the potential of being a high traffic monitized site for any size business.