“Self-hosted WordPress” means running the full version of the WordPress software on your own web hosting account with your own domain name.
It’s not the free site at WordPress.com — the free sites are stripped-down and don’t have all of the features of the full version. Even the paid accounts at WordPress.com aren’t the full version.
Running self-hosted WordPress on your own website gives you full control. You may install any theme and any plugin. You may do whatever you want on your site because you own the whole thing. You could even move it to another web host if you wanted to.
To have your own self-hosted WordPress site you need a web hosting account. That web hosting account includes the tool to install WordPress automatically. You only have to install WordPress once, then you do everything right from your own web-based WordPress admin dashboard.
I like web hosting plans that include free SSL/HTTPS so you can have the secure “green padlock” on your site.