The use of "this" is confusing me in JavaScript

It's not about performance, it's about accessing a property of a specific instance of an object:-

x.init()

Would not display 'test' if you hadn't use this in the function.

Effectively the above line is the same as:-

x.init.call(x);

the first paramater in the use of call is assigned to this when the function is executed.

Now consider:-

var fn = x.init;  //Note no () so the function itself is assigned to the variable fn
fn();

Now you get nothing in the alert. This because the above is effectively:-

fn.call(window);

In browser hosted Javascript the window object is synonymous with the global object. When a function is called "in the raw" then the this defaults to the global object.

The classic error is doing something like this:-

var x = {
   ele: 'test';
   init: function(elem) { 
      elem.onclick = function() { alert(this.ele); }
   }
}
x.init(document.getElementById('myButton'));

However this doesn't work because the function attached to the onclick event is called by the browser using code like:-

onclick.call(theDOMElement)

Hence when the function is running this isn't what you think it is.

My usual solution to this situation is:-

var x = {
   ele: 'test';
   init: function(elem) {
      var self = this; 
      elem.onclick = function() { alert(self.ele); }
      elem = null;
   }
}
x.init(document.getElementById('myButton'));

Note the elem = null is IE memory leak work-around.

It is very confusing. It depends on how you call the function. Doug Crockford did a good write-up in his book Javascript, the Good Parts. The gist of it is in this excellent answer to an otherwise badly formulated question.

And no, it's not about performance.