When I was looking to start a blog I kept seeing every one suggest that if you wanted to be serious about blogging you should self host your blog. Self-hosting refers to your ability to own your blog. If you use a free site, you don't have control over what happens to it.
One of the first decisions you will need to make when starting a blog is whether you or not you want to be self-hosted. Self-hosted means you get to pick your domain and won't see any branding. For example, a non-self-hosted blog domain might be elizabethstapleton.wordpress.com but a self-hosted blog domain would drop the wordpress.com