Shared Links are new to iOS 7. With them, you can see a list of all the links shared by everyone you follow on Twitter, all in one convenient place inside Safari. Think of it as a Reading List populated by people you find interesting. It's a great place to go if you have time and are looking for something serendipitous to read, but you have to know where to look if you want to find it.
That's all there is to it. Shared Links is one easy to use place to manage all your links. Currently Twitter is the only kind of link supported but we'd imagine over time we may see Apple expand the service to others as well. You can also use Shared Links in Safari for OS X Mavericks, so make sure you check that out as well!
Note: If you don't see anything under Shared Links, go into Settings > Twitter and make sure you're signed in.