What is ‘self-hosted’ WordPress?

WordPress comes in two flavours: self-hosted and hosted.

A self-hosted WordPress site is one where you, the website owner, has arranged for your site to be hosted e.g. with WPEngine, BlueHost etc. The WordPress CMS software is installed on the hosting space you’re paying for and all the content you post on the site is completely owned by you.

A hosted WordPress site is one where you don’t make use of, or pay for, your own hosting space – your website is hosted by WordPress at their domain wordpress.com e.g. yoursite.wordpress.com

There are advantages and disadvantages to both options:
Self-hosted
You can use your own domain e.g. yoursite.com
Typically hosting is charged for so there is a cost
You have complete control of the website – it’s look, feel, features, customisation – everything!