When do I need to use JSON and XML?

I know there are a lot of sources which explain this, but they just talk about storing key/value pairs in an array or in an object.

I can't understand why or when should I do this, although I always use jquery's AJAX. As an example, if I make a forum when do I need this? Can someone give real world examples?

The same goes for XML. It stores information too. But what kind of information? Why can't I store it in MySQL?

EDIT: so with $.json() you retrieve a json file and then display the content in the browser. but who creates this json file? me? manually? and why? and how?

so you can just retrieve a json file? can you do something else?