These are supposed to generate an instance agnostic link regardless of who clicks it. That means they’ll go to their instance’s version of your page, which means they can subscribe or whatever with their logged in account. Rather than going to an entirely different instance, then having to manually search for it in their own instance. However, the caveat is that not all apps have adopted these links - they work on the website, but not all of them work in Jerboa, for example.
There’s also @user@instance, this doesn’t automatically make a link but if you start typing it (on the website) then you’ll get a popup window with usernames. When you select this you’ll generate the code @user@their_instance. This links to the user’s instance, not the viewer’s instance, but it also sends a mention to the user. So if you reply to another user and mention them, they’ll get a notification. I think you can also fiddle with the link text with like [link text](https://their_instance/u/user) and it should still send a mention, but haven’t tested it.