Very simple, from the source:
Lemmy Universal Link Switcher, or LULs for short, scans all links on all websites, and if any link points to a Lemmy instance that is not your main/home instance, it rewrites the link so that it instead points to your main instance.
In essence, any Lemmy link you come across is automatically redirected to your home instance. It’s also easy to customise, you can add/remove instances and prevent it from working on particular sites (or force it to only work on sites you wish).
Can be installed with Tampermonkey or ViolentMonkey (or similar tools).
note: this may also work just fine on mobile browsers that support extensions (and would likely help direct your browser to opening your lemmy app - if you have one - more often), but I haven’t tested this.
Also, if nobody on your instance has ever visited that sub or instance, redirecting to your home will kind of make contact with them so it shows up for other people in your instance.
Idk if I’m explaining correctly, but federation only works if you opened it on your instance, without it, you will never find that content.