Perhaps the extension doesn't have the best name because its primary purpose is to handle the redirects to the canonical domain (or "origin", as it's domain+protocol). This is very much something you need to do, or search engines will punish you and you might have infrastructure issues if your users are not all using the same domain to access your website. In the case of Flarum, the app usually doesn't work at all if you try using it from the incorrect domain.
However using the extension to achieve this redirect should be a last resort, because there are many more efficient ways to achieve it. Depending on your hosting, it might already be done out of the box and having the extension just slows your forum by a tiny amount while doing absolutely nothing. I wrote those warnings at the top of the README for the extension 
#19307 The other common method is the use of htaccess rewrite rules or the equivalent nginx rules.
The canonical path, which is also something search engines care about, is a different concept already handled by Flarum via the HTML meta canonical tag. The "Canonical Url" extension has no impact on that.
