Fandoms and Worlds:
Many fangirls and fanboys identify the time and place that their fandom occurs as that world, such as middle earth, Hogwarts, Victorian England with demon servants... The "world" also features characters and history. My spin on it is that every fandom has a world, and every world exists.
A Link Between Worlds:
Sorry to let you down, but this strictly means as in your spiritual link. You have a minimum of one link per world. They are your character (whether determined you relate with them the most, look the most like them, or even favour them and make the choice on your own that they are your link.)
The Vault: Links:
The Vault is a common-room for all links to meet each other. This is a place where worlds and dimensions collide to form a nice lounge area. That way, your cross world ships can come true! You can also interact with other people's links and the other sides of you.